OTC 4586

Gulf of Shallow-Water Wave Heights and Forces Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 by R.G. Bea, PMB Systems Engineering Inc.; N.W. Lai, Woodward Clyde Consultants; A.W. Niedoroda, Dames & Moore; and G.H. Moore, McMoRan Offshore Exploration Co.

This paper was presented at the 15tb Annual OTC in Houston, , May 2-5, 1983. The material is subject to correction by the author. Permission to copy is restricted to an abstract of not more than 300 words.

ABSTRACT tinental Shelves. General guidelines for setting environmental criteria (e.g., API RP 2A) have Storm waves tend to be attenuated by a variety been developed in the past to provide broad ranges of processes as they propagate across the relatively of possible design values. These guidelines, shallow depths of the Texas and Continental however, have generally neglected detailed considera­ Shelves. Present shallow water wave force guidelines tions of shallow water effects on storm waves. contained in API RP 2A were developed as a very simplified, judgment-based interpolation into water In late 1981, McMoRan Offshore Exploration depths less than 300 feet. Shallow water design Company initiated a study of environemtnal criteria wave force levels adopted by many companies generally which could be applied to platforms in relatively reflect the conservative adjustments made after shallow depths in the western . many platform losses and significant damages were This study was organized in two parts. The objective incurred during in 1964. Subsequent of the first part was to develop and calibrate tests of the new generation of shallow water platforms a procedure for determining the amount of storm by other hurricanes indicates acceptable performance wave height reduction due to dissipation of wave of the structures. However, costs associated with energy through fluid shear stresses acting on these structures, as well as results of some of the seafloor of the continental shelves. The the more recent studies, indicate that there may prime consideration was wave attenuation due to have been some degree of over-correction in the the effects of bottom friction, although some process of revising the industry's shallow water attention was given to the effects of refraction, criteria after Hurricane Hilda. shoaling, energy loss due to flow within the bottom sediments, and other effects. The purpose of this study was to develop a rational procedure for establishing environmental The second part of this study consisted of design conditions for platforms in relatively shallow a wave force parameterization procedure. The water in the Gulf of Mexico. This paper discusses objective of this part of the study was to quantify two parts of this study. The first part is that the recurrence intervals of storm-related events of developing and calibrating a procedure for determin ngn terms of the resultant base shear and overturning the amount of storm wave height reduction due to moments on typical 8-leg, steel jacket structures dissipation of wave energy through fluid shear stresse in representative areas of the western Gulf of acting on the seafloor of the Continental Shelves. Mexico. A study of the base.shear and overturning The second part is that of developing and justifying force data with the input environmental data on a wave force parameterization procedure to quantify waves and currents, resulted in the development wave force levels on typical jacket structures in of a series of guidelines for determining the the Gulf of Mexico. environmental loadings on future platforms to be sited in these regions. INTRODUCTION This paper has been released by McMoRan as The development of a rational system for esta­ general interest and to suggest the need for future blishing environmental design criteria for platforms research to develop more definitive shallow water in relatively shallow water in the Gulf of Mexico criteria. requires an investigation of the phenomenon related to storm wave propagation over Continental Shelves. DEEP WATER WAVES It is known that storm waves tend to be attenuated by a variety of processes as they are driven across The maximum wave height which can reasonably the shallow depth of the Texas and Louisiana Con- be expected to affect a structure during its life­ time is one of the most critical factors which References and illustrations at end of paper. influences the design of an offshore structure. 49 2 GULF OF MEXICO SHALLOW WATER WAVE HEIGHTS AND FORCES OTC 4586

The estimation of such maximum wave occurrences SHALLOW WATER WAVE HEIGHT ATTENUATION in the future must reflect the past history of storm wave occurrences. Thus, long-term historical data The maximum wave height statistics discussed bases are required to estimate these maximum wave in the earlier section have been restricted to height occurrences with meaningful reliability. deep water regions where the waves do not feel the effect of the ocean bottom. As the waves Characterizations of historical storm conditions propagate into shallow waters, the wave heights can be either based on measured or hindcast data. change due to wave transformation and bottom dissipa­ However, since only relatively small amounts of tion of wave energy. The wave transformation measured wave data are available in the Gulf of in shallow waters includes shoaling and refraction Mexico, hindcasting techniques are necessary to effects. The wave energy dissipation mechanism extend the data base. A hindcast is the reconstruc­ may consist either of bottom friction, percolation tion of an historic event or series of events to or soft-bottom interaction, or combinations of yield certain meteorological and/or oceanographic the three and other unknown factors. Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 data for the study area. Through the reconstruction of these events, a series of data can be generated. Shoaling A statistical analysis can be conducted with the hindcast data to provide estimates of future occur­ As a wave propagates from deep to shallow rences. water, its height and length change. The transformed wave height, H, at shallow water dept relative The deep water maximum wave conditions obtained to the original deep water wave height, H , can in this study are based on historical hindcast studies be computed from: 0 of Gulf of Mexico hurricanes. The hindcast deep water wave heights are shown in Figure 1.

The probabilistic distribution of expected deep water maximum wave heights has been based on where V is the group velocity of the waves, b results published by Bea (1974), Ward, et al (1978), is the distance between pairs of adjacent wave and Haring and Heideman (1978). The 100-year deep rays, and the subscript o refers to deep water water expected maximum wave height at an average condition. site in the northern Gulf of Mexico is indicated to fall in the range of 70 to 72 feet. This value The term (V /V)~ is also known as the shoaling is comparable to the API Reference Level Height coefficient, K •0 The shoaling coefficient is of 71 feet in a water depth of 400 feet for the given accordin~ to linear wave theory by open, broad, Continental Shelf of Western Louisiana and Eastern Texas (API, 1981).

Characterizations of wave periods associated with maximum wave conditions are important as they can have significant effects on the computation where h is the water depth and k is the wave number. of wave forces on offshore structures. A study K' is then given explicitly as a function of wave of the joint probabilities of wave height and period l~ngth and water depth. in hurricane· conditions has been reported by Earle, et al. (1974). The study was based on a wave­ Wave Refraction by-wave analysis from data obtained during from the Ocean Data Gathering Program. Earle, The term (b /b)~ in the shoaling equation et al. reported that height-period joint probabili­ represents the rglative spacing of adjacent wave ties are time dependent, with large relative wave rays and is also defined as the refraction coefficient periods becoming less probable as the hurricane ~· Physically, the relative spacing between and its extreme waves pass the site. wave rays represents the local wave energy density. It is generally assumed that the wave energy contained The hindcast results of Haring and Heideman between wave orthogonals is conserved as the wave (1978) show that a representative wave steepness front progresses. Various graphical and numerical (ratio of wave height to length) of 1/13 for deep methods are available to compute wave refraction. water and 1/12 for relatively shallow water can In this study, the graphical procedure was adopted. be generalized for hurricane wave conditions. These However, most of the wave paths were near normal wave steepness ratios correspond to wave periods to the smoothed depth contours; thus, the wave of about 12 to 13 seconds. A wave steepness of refraction effects proved to be insignificant. 1/12 is also recommended in API RP 2A for the Gulf of Mexico area for the determination of design wave Bottom Friction periods associated with the API reference level wave heights. Wave energy lost through bottom friction results from the work done by the wave orbital Based on the above sources, the extreme wave velocity against bottom shear stress. The bottom heights are expected to be associated with "growing" stress can be expressed as: sea states in which waves are relatively steep with shorter wave periods. The longer period waves are usually associated with the more regular swells that have traveled some distance, but are usually lagging behind the peak of the storm. Thus, wave where ' is the bottom shear stress, p is the density periods associated with the maximum design waves of water, f is the wave friction factor and u are suggested to be on the order of 12 seconds. is the flui~ velocity immediately outside the bottom 50 OTC 4586 R. G. BEA, N W. LA!, A. W. NIEDORODA, and G. H. MOORE 3

boundary Layer. Laboratory and semi-theoretical and Reid (1954) combined this form of energy dissipa­ studies by Jonsson (1965) indicated that f is a 2 tion with friction and refraction to modify water function of both the wave Reynolds number ~defined wave heights. According to Hsiao and Shemdin by R = aum/v), and the relative roughness (defined (1978), who summarize the present knowledge on by a/K ). The parameter a is the maximum displacement bottom dissipation, the pressure field induced of botfom fluid particles from the mean position, by wave motion in a permeable sand layer is governed u is the maximum wave orbital velocity outside by Laplace's equation tWe bottom boundary layer, v is the kinematic visco­ sity, and Ks is the bottom roughness height. For a flat ocean bottom with noncohesive sediments, the bottom roughness height, K , can be estimated directly from the mean diamete~ of bottom sediments. where P is the pressure in the sand, a and S

When bottom conditions are such that ripples are the horizontal and vertical coefficients of Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 are formed, the bottom dissipation will be enhanced permeability, and x and z are the horizontal and due to increased form drag. Additional energy dissi­ vertical coordinates with z in the upward direction. pation occurs in the vortices formed above the ripple The solution that satisfies the equation and the troughs. Dingler (1975) has formulated a relation­ boundary conditions is ship for the ripple formation under certain wave conditions. The condition for the onset of sediment motion suggested by Dingler has the form:

where d is the thickness of the sand layer, w is the wave frequency and k is the wave number. The rate of energy dissipation can be shown to be where y = (p -p)g, p is the density of sediments, T is wa~e per~od, D ~s the mean sediment diameter, ~is the viscosity o~ water, and g is the gravitational acceleration. If this condition is satisfied, bottom ripples can be expected. where w' is the vertical fluid velocity in the sand. Combining the above relations, a general Dingler indicated that ripple slopes were a equation to compute the wave energy dissipation function of a dimensionless stress parameter, es' due to percolation can be obtained as defined in terms of wave orbital velocity and bottom sediment properties as follows:

Using this dissipation equation, the dissipation The ripples were found to become 2nstable and vanish rate can be computed for different water depths. for cpnditions when 9s ~ 2.5 x 10 • Nielson (1977) Hsiao and Shemdin (1978) indicate that wave energy reported a different characterization of ripple dissipation due to percolation can be more significant properties by correlating a set of dimensionless than friction dissipation due to drag at the seafloor ratios y /a and u /W, where y is the ripple wave for coarse sediments in deeper water. length aRd W is tWe sediment ~all velocity. In the range where the bottom fluid shear stress is The above described formulation for percolation greater than the value needed to initiate ripples, dissipation was also included in the wave attenuation the ripple height and length can be obtained based computer model as a separate dissipation routine. on experimental results. The bottom roughness height, K , for the rippled bottom, taken to be four times Bottom Motion Dissipation t~e ripple height (Hsaio and Shemdin, 1978), can then be calculated. Similar correlations are also When the bottom sediment is composed of soft obtained by experimental results reported by Bagnold mud or decomposed organic matter, the bottom responds (1946), Inman and Bowen (1963), Jonsson (1966), to the wave-induced pressure field in a visco­ Cartsens, et al. (1969), Reidel et al. (1972), and elastic manner. Excessive attenuation of wave Grant and Madsen (1982). energy in the Mississippi Delta area has been attributed to this dissipation mechanism by Gade By knowing the wave Reynolds number and bottom (1958), Bea (1974), Tubman and Suhayda (1976), roughness height, the wave friction factor can be Schapery and Dunlap (1978) and others. estimated from the wave friction factor relations such as that proposed by Jonsson (1965). The average energy transmitted through sea/sedi­ ment interface per unit area and time over one Percolation Dissipation wave cycle can be given by

Pressure variation at the seabottom resulting from surface wave motion can induce cyclic flows in a permeable seabed. The movement of water in and out of the permeable bed can dissipate wave where T is the wave period, P is the wave-induced ~n~rgy. Putnam (1949) was the first to report on bottom pressure, and dh and dt are an infinitesimal this wave energy dissipation mechanism. Bretschneider increase in the height of the interface and time. 51 4 GULF OF MEXICO SHALLOW WATER WAVE HEIGHTS AND FORCES OTC 4586

Based on the general characteristics of a set of ocean current data from three locations in the field experiment data, Suhayda (1977) derived the Fulg (Hall, 1972). Wave height measurements were rate of energy loss due to the soft-bottom motion also recorded and analyzed. Maximum significant in terms of proportionally constant and phase angle wave height and period for the three stations difference. A general equation to compute the soft­ were obtained for Hurricane Anita (1977). bottom dissipation is suggested by Suhayda as The Conoco Test Structure Program (Ohmart, et al., 1970, 1979) is another source where actual hurricane wave measurements were made on an instru­ mented platform. Significant wave height and period and wave force data were obtained for Hurricane where M is the proportionality const&nt between Carmen (1974). the amplitude of the mud wave and the pressure wave, and ¢ = 180° - e, where e is the phase angle between Conoco also has a program jointly sponsored Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 the crest of the bottom pressure wave and the crest with the to provide real of the mud wave. Based on the East Bay study conductei time environmental data, including wave height by Suhayda (1977), values of M = 0.0833 and¢= information during hurricane conditions to the 22° were suggested. The above empirical formulation general public (Bujnoch and Roberts, 1981). This for bottom motion dissipation was included as one program generates wave height data from six stations of the dissipation routines of the wave attenuation across the Gulf of Mexico. Data were obtained program. for (1980).

HURRICANE WAVE ATTENUATION CALIBRATION Inferred wave data were mainly compiled from published sources. Data for The wave attenuation model that was developed (1974), Hilda (1964), and Carla were obtained. in this study was calibrated by running a series These data were basically inferred from damage of hindcasts on ten recent hurricanes and comparing inspection reports that were filed after the passage the results with wave data measured in these hurri­ of hurricanes. Usually, the wave crest elevations canes at various platform sites in different water were noted from equipment or structural damages depths across the Texas-Louisiana offshore areas. observed on the platform deck level. The storm Maximum deep water wave conditions were first re­ conditions were then reconstructed and the maximum constructed for these hurricanes. These maximum wave heights that were associated with the wave deep water waves were then propagated towards shallow crest elevations noted were computed with an appropria e water areas along wave paths, and attenuated by wave theory. the wave attenuation scheme that has been described. The atenuated wave heights were then compared to The approximate locations of all the data the measured data. Adjustments were made in conduct­ stations are shown in Figure 2 with different ing the wave attenuation runs by changing the input symbols to designate the measured and inferred sediment parameters and trying different combinations data. Most of the data are concentrated in the of the bottom friction, percolation and bottom motion Louisiana offshore areas and are in relatively dissipation routines until a consistent set of wave shallow water depths. A total of about 80 data attenuation patterns was obtained. points was obtained for this study with the majority being inferred data. Of the many actual wave Wave Height Data measurement records examined, only the maximum wave heights or sea state conditions recorded A significant amount of wave height data is throughout the storm were used. Thus, all the available for the shallow water attenuation calibra­ data points used in this study represent the maximum tion. The data fall into two categories, that which wave height conditions existing on those platform was actually recorded by wave staffs installed on sites that were associated with particular hurricanes. offshore structures and that inferred from damage inspections on platform structures after the passage Significant wave heights were used in the of hurricanes. hindcast calibration study. Review of the continuous wave records obtained from several severe hurricanes One rich source of data utilized in this study indicated that the maximum wave heights were most was the Ocean Data Gathering Program (ODGP), a joint often associated with the maximum significant industry project, which has wave height measurements wave height condition. Such sea states at various for hurricanes since 1968 (Hamilton and Ward, 1976). sites persisted in the range of 2 to 4 hours, This program includes wave staff recordings on six or for about 1,000 wave cycles. Assuming that platforms across the Gulf of Mexico. Some of the the wave heights were Rayleigh distributed, as recorded storm data have been made public through foundy by Bretschneider (1964), Goodknight and the National Climatic Center. Storm reports that Russell (1963) and Collins (1967), the maximum were collected for this study are for Hurricanes wave height to maximum significant wave height Edith (1971); Celia (1970); Laurie (1969); and Camille ratio would be about 1.9 for 1000 waves. This (1969). These reports contain continuous wave height approximation was used to convert the maximum recordings at the six stations and provide maximum wave heights inferred from wave crest elevation significant wave height and period information from data to maximum significant wave heights. the analyzed data. Wave Hindcast The Ocean Current Measurement Program (OCMP) is another source of storm wave data. The instrumen­ A calibrated hindcast reconstruction of the tation program was originally installed for obtaining deep water sea state conditions associated with

52 OTC 4586 R. G. BEA, N. W. LAI, A. W. NIEDORODA, and G. H. MOORE 5 each of the hurricanes and associated wave data dissipation mechanisms available in the computer collected was obtained as discussed earlier. Neces­ model were tested. It was found that only the sary hurricane parameters such as central pressure, bottom friction model cnuld produce wave attenuation radius of maximum wind, and storm track information, patterns that were consistent to the wave data were obtained from sources such as the National obtained from measurements and observations. Initial­ Hurricane Center, Corps of Engineers Storm Reports ly, a uniform average sediment size was assumed for the individual hurricanes, and Ho, et al. (1975). for the entire wave propagation path. Attempts Significant wave heights were then hindcasted for were also made to vary the input sediment sizes twelve deep water locations (Figure 2). These loca­ along the attenuation paths according to the actual tions represent the originating areas for the waves bottom conditions as shown on the surface sediment that propagated into the shallower water depths maps. However, it was found that this approach where the wave height data points are located. A did not improve the quality of the wave attenuation time history of significant wave heights was con­ hindcast. Further experimentation showed that structed at each of these twelve locations. A direc­ the quality of the hindcasts could be improved Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 tional distribution of wave heights was also con­ by adopting an equivalent sediment roughness length structed. The maximum significant waves and asso­ factor based entirely on the degree of agreement ciated wave period were then selected for calibra­ between computed wave heights along the wave path tion, together with their directional information. and the corresponding field data. In this way, the equivalent sediment roughness lengths were Most hurricanes in the Gulf of Mexico produced treated as an empirical factor which controlled maximum waves from the southeast quadrant approach the amount of bottom energy dissipation acting direction. The paths along which the minimum loss on the computed waves to obtain good fits with of wave energy can take place are those running the data. This approach was adopted for the final normal to the bottom contours. Wave propagation calibration. paths from the twelve deep water sites were construc­ ted roughly normal to the general bottom contours. Calibrated attenuation runs for selected These paths were then extended into the shallow hurricane wave data cases (Audrey, 1957; Hilda, warter to synthetic wave data locations (Figure 2). 1964; Carmen, 1974; Alan, 1980) are shown in Figures 3a through 3d. The attenuated wave patterns and WAVE ATTENUATION CALIBRATION locations of observed data are plotted in each case. The deep water hindcast wave heights and As shown in Figure 2, the Gulf of Mexico was periods, and the equivalent sediment roughness divided into three regional areas for the calibration length used in each case are given in Table 1. study (denoted A, B, C). Region A includes offshore areas from South Padre Island northward to the Brazos Due to uncertainties involved in the conversion area. The shoreline and bottom contours are aligned of maximum wave heights to significant wave heights, approximately north-northeast to south-southwest the inferred data are shown as a bar spread using in this area. The bathymetry is quite uniform with a possible range of maximum wave to significant the 60 foot water depth contour close to shore and wave ratio of 1.5 to 2.2. The expected values the 600 foot (Nominally the edge of continental based on a maximum wave to significant wave ratio shelf) contour approximately 55 miles offshore. for 1.9 were shown as a solid dot on the bar spread. Region B runs from the Galveston area to the Vermilion The approximate breaking wave height limit is area. The deep water (600 foot) contour is aligned also shown on each attenuation plot as the upper approximately east-west and is quite far from shore limit of shallow water wave heights. A summary (approximate average of 90 miles). Region C covers of the parameters used in the final comparisons areas from South Marsh Island to the Mississippi with observed data were achieved by ~~ing equivalent River Delta area. Here, the continental shelf is sediment roughness lengths of 4 x 10 f~~t. (about aligned approximately northeast-southwest. The 0.12 mm) for Region A and B, and 10 x 10 feet bathymetry changes rather rapidly and the bottom (about 0.30 mm) for Region C. contours are relatively convoluted. There is little separation between the 60 foot and 600 foot contours, In order to quantify the quality of calibrated especially near the mouth of the Mississippi River. attenuation results, the comparisons are expressed as ratios of observed maximum wave heights to Bottom sediment information was obtained from hindcast maximum wave heights. These ratios are surface sediment charts of the Gulf of Mexico prepared ranked and plotted on log-normal probability paper by Grady (1970) and Berryhill (1981), and the Bureau in Figure 4. The data were divided into three of Land Management OCS Lease Sale Environmental sets according to water depths: 300 to 150 feet, Statement Reports. The patterns of sediment distri­ 150 to 75 feet, and 75 to 0 feet. Best fit lines bution is complex. In general, surface sediments through all the data are shown together with the in Region A can be described as mainly silty clay 96 percent confidence area. The log-normal distribu­ with silt and sand strips and pockets distributed tion appears to be an acceptable description for along the very shallow areas. Region B is predomi­ the comparison data. Note that the 50th percentile nantly silty sand and sand. In Region C, surface values in all three water depth ranges are very sediments are predominantly clayey materials with close to 1.0, 95 percent of the values are indicated very soft sediments, especially around the Mississippi to fall in ranges of 0.9 to 1.3 for the deeper Del.ta area. waves, 0.85 to 1.3 for the intermediate waters, and 0.85 to 1.5 for the shallower waters. Consider­ During the calibration exercise, the hindcast ing that the data are not perfect and theoretical deep water wave heights were attenuated along the principles have been approximated in the wave prescribed paths through Regions A, B and C, starting attenuation procedure, these plots indicate that from a water depth of 600 feet. The different energy the wave attenuation model can produce results of acceptable accuracy, comparable to other parts 53 6 GULF OF MEXICO SHALLOW WATER WAVE HEIGHTS AND FORCES OTC 4586 of the wave and current hindcasting, wave force (e.g. currents, drag, and inertia coefficients, determination and criteria selection procedures. kinmatics theory), they resulted in wave forces substantially in excess of those implied by these Based on tre equivalent sediment roughness results. length that was used in the calibration study of wave attenuation in Region C as compared with that Wave Force Computations in Region A and B, one must conclude that other bottom-wave interaction processes are active in Wave forces were computed on four McMoRan Region C. Region C actually is one that would have platforms located in Eugene Island A-315, High the smaller sediment size as compared with Region Island A-471, Matagorda Island 713 and Matagorda A and B. It is suspected that movements of the Island 555. These platforms are located in water soft bottom sediments likely are responsible for depths of 240 feet, 189 feet, 109 feet and 75 the additional energy dissipation presently represente feet, respectively. All four structures are typical,

in the larger equivalent sediment roughness length. eight-leg, fixed bottom drilling and production Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 The unsuccessful attempt of using the bottom motion platforms with 14 conductors. dissipation routine in the wave attenuation model to hindcast shallow water wave heights in Region Computations were performed by using a proprie­ C probably reflect the need for a better model to tary, three-dimensional wave load generation computer simulate this form of energy dissipation. It should program. This program is similar to most of the also be pointed out that the best fit equivalent existing wave load programs used by the offshore sediment roughness lengths in the calibrated runs industry. The program first computes fluid particle should be treated as a form of empirical sediment kinematics (velocities and acceleration) for given factor that would produce a level of friction energy sets of wave conditions using a selected wave dissipation equivalent to the actual physical condi­ theory. An option is provided to allow the program tions. The actual physical conditions may include to select the most appropriate wave theory based a certain combination of different dissipation effects on the input wave conditions. such as friction, percolation, bottom motion, wave­ current interactions, wave-wave interactions, effects The Stokes Fifth Order Theory was applied of adverse winds, three-dimensional sea state condi­ to steep waves in deep water. For large waves tions, and other unknown factors not accounted for in shallow water, the Stream Function Theory was in this study. applied.

Shallow Water Wave Characterization Wave forces acting on structural members were computed through the Morison Equation. Waves After the representative quivalent sediment were stepped through the structure such that the roughness length for Regions A, B and C were deter­ varying wave forces could be determined for different mined, the wave attenuation model was used to atten­ positions of the wave. Current forces were accounted uate the deep water maximum design level wave heights. for by superimposing a prescribed current velocity profile onto the computed wave kinematics profile. Plots of the range of attenuated wave heights Wave forces on inclined members were treated by for a 100-year site return interval for the three retaining the normal components of water particle regions are shown in Figure 5. In each case, differ­ velocity and acceleration acting on the members ent attenuation paths were computed for different and discarding the tangential kinematic components, locations and various approach directions within although other alternatives are possible (Wayde the regions into the shallow areas. A spread of and Dwyer, 1976). attenuated wave height variabilities was shown in each case to represent the geographical differences The program provides different options for within the regions and the relative amount of refrac­ describing the input drag and inertia coefficients tion effects that may exist. The amount of wave such as varying with water depth and member size, refraction depends on water depth and bottom contour or constant coefficients specified by the user. orientation, as well as the direction of wave approach relative to bottom contours. The program computes the horizontal and vertical velocity and acceleration profile; the horizontal Also, plotted in Figure 5 are the API guidelines and vertical drag and inertia pressure profile; reference level wave height and the 100-year atten­ and the total horizontal and vertical pressure uated wave height curve obtained from Haring and profile. The program then searches through the Heideman (1978), compared to the wave attenuation computational steps and selects the maximum resul­ patterns obtained from this study. Results indicate tant base shear and total overturning moment acting that attenuated shallow water wave heights developed on the structure. from this study are comparable to the API reference level wave heights, and are consistently lower than Wave Force Comparisons that obtained by Haring and Heideman. Maximum resultant base shears and total over­ The design wave height curve utilized by McMoRan turning moments on the platforms at the four water pre-1982 also is indicated in Figure 5. A deep depths described in the above section were computed water wave height of approximately 57 feet is indi­ for the wave and current conditions obtained from cated. A design wave height of 53 feet is indicated this study (Approach No. 1), the API reference for a water depth of 100 feet. As will subsequently level (Approach No. 2), and that used by McMoRan be discussed, even though the McMoRan pre-1982 wave pre-1982 (Approach No. 3). heights generally were substantially lower than those of this study, of API, and of Haring and Heidem

54 OTC 4586 R. G. BEA, N. W. LA!, A. W. NIEDORODA, and G. H. MOORE 7

A, B, and C, and for each of the four water depths shallower water depths. However, these shorter (240, 189, 109 and 75 feet). The API reference wave period base shears increase markedly in deeper level and the McMoRan pre-1982 wave criteria are water, and eventually give a higher force level also listed in Table 2. than the longer wave period forces.

Approach No. 1 The overturning moments behave in a similar fashion to the base shears with smaller force The 100-year wave heights from this study used levels associated with shorter wave periods in to compute wave forces are the average wave heights the shallow waters and then a reverse of this obtained from the calibrated wave height attenuation trend in deep waters. However, the shorter period results for regions A, B and C. The wave forces overturning moments overtake the longer period were computed by using a constant drag coefficient values at a much shallower water depth than the of 0.6 and a constant inertial coefficient of 1.5. base shears. The overturning moment plots do Forces were computed with and without current for not show a similar distinct peak at the 100 foot Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 a range of wave periods (11, 13 and 15 seconds). water depth level, but tend to increase steadily and more rapidly with greater depths. Approach No. 2 The range of currents defined in this study The API wave forces were computed by using (not discussed due to space limitations) combined the reference level wave height (Figure 5). In with the wave heights generally results in increasing general, this reference level wave height is intended the maximum resultant base shears on the structure for the open, broad, continental shelf of Western by 30 to 40 percent. The addition of currents Louisiana and Eastern Texas (API RP 2A). A wave also increases the overturning moments by about steepness of 1/12 associated with the reference 20 to 40 percent, with the effect becoming more level wave height is recommended for offshore Gulf pronounced with deeper waters. of Mexico, giving design wave periods of about 12 seconds for the four water depths. As specified, The API reference level and the McMoRan pre- no currents are included in the API reference level 1982 design wave force plots are shown in Figure criteria. Constant drag and inertial coefficients 9. Also shown are the results from this study of 0.6 and 1.5 for members 6 feet in diameter or for the 100-year wave force plots averaged over less are also recommended for the API wave force regions A, b and C that are computed for the 13 computations. second period wave without the currents.

Approach No. 3 The resultant base shear associated with the 13 second period wave is very similar to the The wave heights are summarized in Figure 5. API reference wave force level, with a maximum These wave heights were used with a wave period difference of about 6 percent between the two of 16 seconds. Currents were included in all wave at around the 100 foot water depth. This is expected, computations in the range of 2.6 to 3.4 fps at surface as the wave heights and periods and other criteria decreasing linearly to 0.4 fps at the sea floor. in both cases are similar. The drag and inertial coefficients vary with water depth and member sizes. The drag and inertial co­ The McMoRan pre-1982 wave force is consistently efficients generally fell in the range 0.65 to 0.75 much higher than both the API and those from this and 1.4 to 2.0, respectively. study. The maximum base shear for the McMoRan pre-1982 design condition is about 35 percent Marine fouling was considered in all cases and 44 percent higher than the API and Approach by increasing the structural members' radii by 1 No. 1 base shear levels, respectively, at the inch. The Stokes Fifth Order Wave Theory was used 100 foot water depth. This can be explained by in all cases for the 240 and 189 foot water depths, inclusion of currents, longer wave period, and while Dean's Stream Function Wave Theory was used larger drag and inertial coefficients in Approach for the 109 and 75 foot water depths. No. 3.

Wave Force Computation Results SHALLOW WATER WAVE FORCE CRITERIA SELECTION

Wave force versus water depth (and overturning Selection of shallow water wave force criteria moment vs. water depth) plots for Approach No. 1 should be the prerogative of the platform owner. for the 100-year wave conditions are summarized That is, decisions affecting safety and economics in Figures 6 to 8 for regions A, B and C. Shown of a platform system should be made by those that in each plot are the wave forces for the 11, 13 must bear the direct consequences of those decisions. and 15 second wave periods with and without the The technologist can provide information and data current contributions. on which to base such decisions. The quality of the decisions will be dependent on the quality In general, the maximum base shears vary with of the input to such decisions. water depths in a distinct pattern in which the base shear increases rapidly with water depth in This study was intended to develop sufficient shallow water, reaches a peak at around 100 foot insights into shallow water wave force conditions water depths, drops to a low level at about the so as to allow adoption of wave force design criteria 200 foot water depth, increases mildly and then that were close to those of the API Reference tends to level off as it gets into the 250 to 300 Level. One primary aspect of such criteria was foot water depths. The base shears computed for studied in detail: wave-bottom interaction leading the shorter wave periods are usually lower in the to decreasing wave h~ights in shallow water. A theoretical procedure was implemented and calibrated 55 8 GULF OF MEXICO SHALLOW WATER WAVE HEIGHTS AND FORCES OTC 4586 with measured and observed data from past hurricanes. as a stochastic process affecting the regions. The primary result developed was that wave heights Thus, some form of a compromise is necessary. can decay much more rapidly than previously thought. (Hsiao and Shemdin, 1978; API, 1981). In this study, the regional probabilities of occurrence of wave conditions in deep water There are a large number of other important were utilized to define return periods associated factors that must be properly assessed before one with given wave heights (and associated periods can spedify wave force design criteria. Given the and directions of approach). Then, these specific API structure and foundation design guidelines, wave conditions were propagated into shallow water it is apparent that in order to develop a next­ utilizing the bathymetric and soil conditions generation wave force criteria procedure, other appropriate for reasonable sub-divisions of the environmental factors must be evaluated and assessed. region. The accuracy of the compromise approach Principally, these factors are: selected for derivation of a procedure for selecting

wave force design criteria is not known, but was Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 Site, area and region wave heights, periods felt to be of sufficient accuracy for purposes and directions of this study.

Site, area and region current speeds, profiles Current Conditions and directions Hurricane current conditions in the moderate Computation of wave kinematics water depths of the northern Gulf are poorly known. While a significant amount of data has been gathered Combination of wave and current kinematics from the industry's measurement programs (Hall, 1972), and complex analytical models formulated Computation of hydrodynamic forces and calibrated (Forristall, 1974), the understanding of hurricane current conditions lags behind the Assessment of design forces (selection of understanding of hurricane wave conditions (Ward, appropriate "return interval conditions," et al., 1978). implying definition of acceptable safety and economics) • What is understood at the present time is that reasonably accurate predictions or hindcasts Definition of design deck elevations. can be developed for coastal surges and for currents in moderate depths, if the wind fields of the As they influence the design wave force objectives, hurricanes are known with reasonable accuracy each of these factors will be discussed in the follow­ (Forristall, 1974; Shemdin, 1972). In this study, ing sections. again a compromise had to be made. This compromise utilized application of a single layer current Wave Conditions prediction model that had experienced calibration based on data from coastal surges and measurements Deep water (water depth greater than about of currents in moderate water depths (Brestschneider, 300 feet) hurrican wave conditions in the northern 1966, 1967, Forristall, 1980). Hurricane wind Gulf of Mexico are reasonably well understood (Bea, conditions associated with the site averaged expected 1980; Marshall and Bea, 1976). Lesser confidence maximum wave height conditions were utilized to is associated with such conditions on the lower make projections of the currents at shallow water Texas coast (Bea, 1974). The industry's measurement sites that could exist at the time of occurrence and the analysis programs (Ward, et al., 1978, Haring of the maximum wave heights (note that both a and Heideman, 1978) have converged on a characteriza­ spatial and temporal relationship exists between tion of the probabilities (or return periods) of the waves and currents that must be predicted wave conditions in deep water. or characterized).

The 100-year expected maximum wave height at The accuracy of this compromise procedure a site in the northern Gulf is in the range of 70 is of the same order of accuracy that backgrounded feet. Variability from site to site caused by the the original API reference level wave force condi­ storm tracks, or directions of approach, and other tions in deep water and is thought to be conservative. storm characteristics would indicate a range from Thus, one could infer sufficient accuracy for 50 to 90 feet at the 100-year return period. This the purposes of deriving this generation of shallow variability is fundamentally irreducible and it water force criteria. Much additional work is is a source of frustration that must accompany site warranted on this point. specific evaluations of design wave conditions. For a generalized design criteria, the suggested Wave Kinematics method is to utilize the expected (or average) site maximum wave height conditions and to accommodate In a conventional design wave force formulation, the variability between sites through factors of long-crested, symmetric, periodic wave shapes safety incorporated into the design criteria. are assumed. Theories such as Stokes, Chappelear, and Stream Function are used to predict the water However, it is on this point that the analyst particle velocities and accelerations of such concerned with shallow water conditions is caught waves. on the horns of a dilemma. While the variability from site to site caused by projected future hurricanep Measurements have been made of the water can qe reasonably treated as a probabilistic process, particle velocities and accelerations accompanying the bathymetric and soil conditions introduce a large waves in storms (winter Northers and hurricanes) site-related bias which cannot be reasonably treated The measurements indicate that as long as the 56 OTC 4586 R. G. BEA, N. W. tAl, A. W. NIEDORODA, and G. H. MOORE 9 basic requirements for wave shape, periodicity and Johansson, 1979; Ohmart and Gratz, 1979). Several directionality are satisfied, then the theories significant efforts have been made to improve will do a reasonably accurate job of describing or extend the basic Morison force theory or model the water particle motions. However, waves associated (Dean and Johansson, 1979; Lai et al, 1980; Hogben, with the intense portions of intense hurricanes 1974). are rarely long-crested, symmetric and definitely are not periodic. The result is that the conventional The efforts to improve the basic Morison wave theories tend to dramatically overpredict the force theory or model have generally met with particle kinematics (Ohmart and Gratz, 1979; Dean limited success. While it is possible to define and Johansson, 1979; Forristall et at., 1978; Bea a more comprehensive and potentially more accurate and Lai, 1978; Nolte and Hsu, 1979). model, it is still necessary to define force coeffici­ ents that are fundamentally empirical in nature. However, before one can proceed to apply such For example, a five component force theory has

an inference to the design wave force issue, the been developed which recognizes: (1) drag (flow Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 methods used to characterize and quantify the non­ separation related to water velocity), (2) inertia wave associated water particle kinematics (due to (pressure effects related to water acceleration, current components) and super-impose these two sources (3) lift (vortex shedding related to water velocity of water motions must be understood. and member flexibility, (4) diffraction (pressure effects related to change in water acceleration Wave and Current Kinematics caused by the size of the body), and (5) relative motion (flow separation related to the motion As previously pointed out, the API Reference of the body in the water). It has been recognized Level Wave Force guidelines do not intend that non­ that the empirical coefficients that accompany wave associated particle kinematics be used; i.e., each of these five components are time-dependent the designer is not to add current velocities to (because the flow-regimes involved are time dependent). those of the wave. The rationale for this comes Significant simplifications must accompany time­ from the over-prediction of wave particle kinematics independent or "average" force coefficients (Lai, and from the inability (at that time) to accurately et al., 1980; Standing, 1981). predict the non-wave particle kinematics. Further, it was rationalized that the wave force measurements In addition, work has been done on "roughened" that were used as an end-point of calibrating the elements to simulate marine fouling (this work overall wave force prediction process contained continues at the present time). Experimental non-wave associated particle kinematics. Thus, results implicate a drmaatic increase in the drag­ through an empirical process, the presence of the related forces with relatively modest amounts non-wave associated particle kinematics and the of roughness (Sarpkaya, 1976). In general, it realities of the wave associated kinematics had is obvious that platform members are marine fouled been recognized. in the Gulf. The amount and extent of fouling depends on the particular marine and platform In this study, a similar line of analysis was environment. Thus, fouling exists. However, used. Wave forces with and without currents were it is not clear how this fouling affects the overall computed on the basis of long-crested wave theory. prediction of wave forces or the prediction of Analysis of the data indicated that if the wave wave forces on individual elements within a platform. associated particle kinematics were reduced so as Again, the measurements indicate that series of to recognize wave energy directional spreading, compensating effects may be developing results and then these kinematics were added to the non- in the real ocean which are quite different from wave associated kinematics, one would develop a those in the laboratory and from the numerical result that was conservatively bounded by the long­ or analytical models. crested wave associated kinematics (without currents). For example, the marine fouling is confined Again, the accuracy of this compromise solution to the upper portions of the platform, where sufficient is not known within the context of this study. It light penetrates to foster development of the can only be stated that the accuracy is thought marine organisms. Measurements of wave kinematics to be consistent with that of the original API Refer­ and forces in this upper zone indicate a dramatic ence Level guidelines and consistent with the results tendency to overpredict both quantities, seemingly of the research and development efforts that have related to the large amount of unaccounted for become available since the time of formulation of turbulence within this zone (Bea and Lai, 1978). the API criteria. The laboratory results have been developed in flow environments that are quite different from Hydrodynamic Forces the actual flow conditions in the near surface portion of a large hurricane wave associated with In the years since the formulation of the API the intense part of the storm. The compromise Reference Level guidelines, there have been very solution allows for the marine fouling by increasing significant strides in understanding the complex member diameter rather than changing the force phenomena of wave forces on individual elements coefficients (drag or lift). and on assemblages of elements simulating full­ scale platforms and elements (Bea dn Lai, 1978; An additional element of the hydrodynamic Ohmart and Gratz, 1979; Haring et al, 1970). Meausre­ design considerations (for extreme conditions) ments have been made on full-scale and 1/4 scale needing some discussion is that of forces on inclined platforms subjected to intense sea states. Sophisti­ members. Analytical studies (Borgman, 1958; Dean cated laboratory measurements have been made to and Harlemann, 1966; Wayde and Dwyer, (1976) indicate determine the relationships between measured water that plausible variations in the method used to particle kinematics and measured forces (Dean and compute wave forces on inclined members can result

57 10 GULF OF MEXICO SHALLOW WATER WAVE HEIGHTS AND FORCES OTC 4586 in significant variations in wave forces on these simplifications are necessary, and the uncertain elements and on the overall platform ( a 25 to 35 must be made certain. The target is the design percent range in the total forces). Theoretical forces that the platform owner desires to have and experimental (Borgman, 1958; Dean and Harlemann, the engineer use in design of the platform. 1966) results tend to indicate that the method which resolves the water particle kinematics to the directio~ An example of such a process for the water perpendicular to the member results in the best depth range of 100 feet is as follows: predictions. These results are best supported by members that have large angles of attach relative 1. Wave height, period and direction: Use to the direction of the water particles (perpendicular results of wave attenuation studies described or 90° to about 60°). Small angles of attach forces in this study to estimate wave heights. are not accurately predicted by this model. For Choose the 100-year wave heights in deep wate purposess of this study and the associated procedure as propagated into shallow water in each of the three regions of the Texas-Louisiana to define design wave forces, the method of resolving Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 kinematics perpendicular to the axis of the member coast studied. Choose the wave directions is suggested for implementation. as appropriate for the expected directions of the paths of the intense storms relative Assessment of Design Forces to the bathymetry of the area. Estimate wave heights appropriate for other directions Definition of the appropriate magnitude of based on the fetch (area of water over which hydrodynamic force to be used in design of a platform winds generate waves) characteristics and intense storm characteristics typical of the is one of the single most serious decisions that must be made by the platform owner. There is no area. Estimate wave periods based on unique procedure that leads to a single best answer. growing waves and field measurements of wave periods associated with the highest waves There are several bases for selection of envir­ accompanying hurricanes in shallow water onmental criteria that have been referred to in (steepness or wave height to length ratios this section. For example, reference to the hydro­ in the order of 1 to 12). dynamic forces defined by the API as Reference Level and to the hydrodynamic forces used by the Industry 2. Current speeds, profiles and directions: Do pre- and post-hurricane Hilda provide bases for not use non-wave particle kinematics in the such judgments. design formulation due to the tendency for the design procedure, (e.g., long­ Referencing the implication of the results crested wave theories) to overpredict par­ of this study in a water depth of about 100 feet, ticle kinematics and the combined procedure the API Reference Level wave forces on a typical to overpredict total wave forces. 8-leg, 14-conductor platform would be about 3500 kips, while that from this study would be about 3. Computation of wave kinematics: Use Stokes 3200 kips. The interpretation possible is that Fifth Order, Chappelear or Stream Function (latter preferred) as appropriate for the the results of this study have been unconservatively interpreted relative to an accepted industry standard. wave and water depth conditions. Do not The question becomes one of whether the accepted introduce a directional energy spreading industry standard is excessively conservative in factor to reduce the particle kinematics in recognition of the large amounts of the range of water depths around 100 feet. directional spreading close to the centers of intense hurricanes that generate design Another point of reference is the pre- and post-Hilda criteria used by operators in the water conditions. Also, do not introduce a surface depth range of 100 feet. Before Hilda, a design turbulence kinematics reduction factor to recognize the inabilities of the hydrodynamic wave force in the range of 1800 to 2000 kips was wave kinematics theories to recognize such used; after the storm a design wave force in the conditions in waves that generate design range of 4000 to 5500 kips was used (referring to conditions. an 8-leg, 14-conductor platform in 100ft of water). The results interpreted from this study imply design Computation of hydrodynamic forces: Use the wave forces in the range of 3000 to 3500 kips, about 4. Morison equation with constant drag coeffi­ double that of the pre-Hilda era. Given the marked cient of 0.6 and inertia coefficient of 1.5. improvements in structural design criteria, inspectior , Do not recognize other force-producing materials, maintenance and safety procedures since components (e.g., lift, interaction due eithe 1965, one might imply that a doubling of the environ­ to their compensating effects or due to mental force criteria is sufficient to provide acceptc~le their unimportance in determining design performance and economy of the platforms. At this condition forces. Compute wave forces on present stage when the technology to make such a inclined members by resolving the wave decision is in development, it is a judgment call particle kinematics perpendicular to the by the platform owner wherein the range of potential longitudinal axis of the members; do not design forces be deems an optimum criteria has been include member shielding or proximity effects achieved. allow for marine fouling by increasing the effective diameter of the members through the Given that one determines for a given type of platform what the desirable design force should marine growth affected zone. be, then a process can be developed to result in Accept a computed total maximum design force that design force. This process is not necessarily 5. on a typical 8-leg, 14-conductor platform unique. It is meant to be realistic yet practical in the range of 3000 to 3500 kips because for application by the design engineer; thus, many experimence and economics indicates that 58 OTC 4586 R. G. BEA, N. W. LAI, A. W. NIEDORODA, and G. H. MOORE 11

this represents an equitable balance of costs the study are acceptable, and that the API guideline and risks to the platform owner. wave forces represent a valid basis for selection of wave forces on shallow water platforms, then CONCLUSIONS the design wave height and force levels resulted from this study can be justified. Substantial The review of the API RP 2A guidelines given reductions in force levels are implicated in comparisor in, the earlier sections of this paper has noted with those utilized before 1982 by McMoRan. that the recommended procedure for determining environ mental loadings on platforms in the Gulf of Mexico Following the completion of this study in was made deliberately borad to account for variations early 1982, McMoRan Offshore Exploration Company in storm conditions in different geographic regions, designed and installed three platforms in shallow as well as a wide range in computational procedures water. Significant savings in costs could be presently used for estimating force levels corres­ directly attributed to the results of this study. ponding to these storm conditions. Furthermore, Further cost savings are anticipated. these guidelines were developed with an emphasis Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 on relatively deep continental shelf environments. FURTHER INVESTIGATIONS The present study has stressed the influence of storm wave attenuation in the mid and shallow contin­ In this study, a rational process was implemented ental shelf regions. to establish environmental loading design criteria for platforms in relatively shallow water in the A computational scheme has been developed and Gulf of Mexico. Numerous theoretical models and calibrated which permits the prediction of shallow engineering procedures were adopted throughout water storm wave heights. The scheme was developed the study. In some cases, approximations and through the application of recently published studies compromise approaches have been used to achieve on the attenuation of ocean waves. However, the results within the limits and scope of this study. scheme has been modified to a semi-empricial technique to provide for the effects of wave energy dissipation The accuracy of these compromise approaches mechanisms which interact to unknown degrees during and approximations are thought to be of the same storms. The primary result developed was that wave order of accuracy that backgrounded the original heights can decay more rapidly than previously thought. API reference level wave force conditions in deep The wave attenuation procedure developed has a relia­ water. Further improvements in the results can bility level comparable with that of the prediction be obtained by considering the following: of w~~e forces on a single member (Lai, et al, 1983). 1. Additional work is required to improve the wave The wave attenuation was ued to hindcast a attenuation procedure. Based on the large variety of actual storm conditions for three sub­ equivalent sediment roughness length that was regions of the western Gulf of Mexico continental used in the study of wave attenuation in Region shelves. The statistical storm wave conditions C as compared with that in Regions A and B, were combined with corresponding current conditions. one must conclude that other bottom-wave inter­ This permitted the development of base shear and action processes are active in Region C. Region overturning moment wave force recurrence interval C actually is one that would have the smaller d~terminations. A study of the resulting environ­ sediment size as compared with A and B. mental and wave force results has permitted the development of a design wave force level similar 2. Additional wave data are required to calibrate to the API reference level for platforms in relative!~ the model, especially for the lower Texas offshore shallow areas. areas where few data are collected for this study. Possible sources are the joint industry measure­ The suggested procedure based on results of ment programs, such as the Ocean Data Gathering this study for computing the design wave force level Program (ODGP), and the Ocean Current Measurement consists of using the method developed in this study Program (OCMP): and the CONOCO hurricane wave to determine attenuated shallow water wave conditions monitoring program. at projected platform locations. The procedure utilizes long-crested wave theory and other conser­ 3. The wave hindcasting method can be improved by vative approaches and, thus, eliminates the need adopting a directional wave spectrum model in for combining the wave forces with non-wave particle which the wave directions and energy distributions kinematics *i.e., currents) in the design formulation. can be treated directly. Such a model has been Stokes Fifth Order, Chappelear, or Stream Function used in joint industry studies by Ward, et al. wave theories are recommended for computing the (1978) and Haring and Heideman (1978). wave kinematics. These wave kinematics are applied to the Morison Equation using fixed drag coefficient 4. The hindcast current conditions can be improved of 0.6 and a fixed inertial coefficient of 1.5. by adopting a calibrated three-dimensional current Marine fouling of structural members in the upper hindcast model such as the one by Forristal (1974) portion of the structure is recognized by increasing Reasonably accurate hindcasts can be developed for the effective member diameters through the marine current in moderate depths by such a model if growth affected zpne. No other hydrodynamic consider the.windfields of the hurricanes are known within ations are made (such as the effect of group members, reasonable accuracy. Currents have potential directional energy spreading, free surface effect, ramifications due to wave-current interaction lift, etc.). The acceptable level of wave forces influences on wave characteristics and resultant on a typical 8-leg, 14-conductor platform is to water column kinematics. be in the range of 3000 to 3500 kips. 5. The more frequent or lower return interval wave Given that one deems the procedures used in force levels obtained in this study (not discussed

59 12 GULF OF MEXICO SHALLOW WATER WAVE HEIGHTS AND FORCES OTC 4586

due to space limitations) were inferred from sta­ Proceedings of the 1983 .Offshore Technology tistics that were complied from hurricane wave Conference. data only. Results need to be improved by considering the contributions of winter storm wave 9. Berryhill, H.L., Jr., "Shallow Surface Sediment statistics. This is expected to have a signifi- Map of Gulf of Mexico Continental Shelf," USGS, cant influence on the more frequent return inter- 1981. val wave heights and force levels. 10. Borgman, L.E., "Computation of the Ocean Wave 6. The selection of shallow water wave force criteria Forces on Inclined Cylinders," Journal of Geo­ in this study was based on a subjective approach physical Research, Amer~can Geophysical Union, in which judgment, experience and engineering Vol., 39, No. 5, 1958. rationale are the primary building blocks. This approach can be extended to a more logical, 11. Bretschneider, C. L. and Reid, R. 0., "Changes systematic and quantitative method by conducting in Wave Height Due to Bottom Friction, Percola­ a reliability and decision analysis. The relia­ tion and Refraction," Technical Memo, Beach Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 bility and decision analysis characterizes the ful Erosion Board, U.S. Army Corps of Engineers, range of potential loadings, examines the pro­ No. 45, 1954. jected platform performance, and attempts to explicitly consider the engineering and manage­ 12. Bugnoch, J.A., Jr. and Roberts, S.C., "The Use ment choices implicated by economic and technolo­ of a Real-Time Weather and Wave Measurement gical considerations. Program to Assist in Offshore Operations," Proceedings, 1981 Offshore Technology Conference, ACKNOWLEDGMENTS OTC 4156, 1981.

Appreciation is expressed to McMoRan Offshore 13. Carsten, M.R., Neilson, F. M. and Altinbilek, Exploration Company for permission to publish this H.D., "Bed Forms Generated in the Laboratory work. In particular, the guidance and assistance Under an Oscillatory Flow: Analytical and of Mr. A. R. Fisher and Mr. S. J. Walton of McMoRan Experimental Study," Technical Memo, Coastal are gratefully acknowledged. Further appreciation Engineering Research Center, U.S. Army Corps of is expressed to McDermott Inc. for their cooperation Engineers, 28, 1968. in supplying the wave force calculations, and to PMB Systems Engineering for support to prepare this 14. Chakrabarti, S.K., "Impact of Analytical Model paper. and Field Studies on the Design of Offshore Structures," International Symposium on Ocean REFERENCES Engineering Ship Handling, Swedish Maritime Research Center, SSPA, Gothenburg, 1980. 1. American Petroleum Institute, "API Recommenden Practice for Planning, Designing and Constructing 15. Dean, R. G. and Harlemann, D. R. F., "Interaction Fixed Offshore Platforms," API RP 2A, Twelfth of Structures and Waves," Chapter 8, Estuary and Edition, January, 1981. Coastline Hydrodynamics, Edited by Ippen, A.T., McGraw-Hill Book Co., 1966. 2. Bagnold, R. A., "Motion of Waves in Shallow Water: Interaction Between Waves and Sand Bottoms," 16. Dean, R. G. and Johansson, P.I., "Rare Wave Proceedings. Royal Society, London, Al87, 1946. Kinematics vs. Design Practice," Proceedings, Civil Engineering in the Oceans IV, Vol. 2, 3. Bea, R. G., "Earthquake and Wave Design Criteria September 1969. for Offshore Platforms," Journal of the Structural Division, American Society of Civil Engineers, 17. Dingler, J.R. "Wave-Formed Ripples in Near Shore ST 2, February 1979. Sands," Ph.D. Dissertation, U.C. San Diego, 1975.

4. Bea, R. G., "Gulf of Mexico Hurricane Wave 18. Earle, M.D., Ebbesmeyer, C. C. and Evans, D.J., Heights," Proceedings, Sixth Offshore Technology "Height-Period Joint. Probabilities in Hurricane Conference, OTC 2110, 1974. Camille," Journal of Waterways, Harbors and Coasta Engineering Division, American Society of Civil 5. Bea, R. G., "Reliability Considerations in Off­ Engineers, Vol. 100, No. WW3, August, 1974. shore Platform Criteria," Journal of the Structur­ al Division, American Society of Civil Engineers, 19. Forristall, G. z., "Three-dimensional Structure ST 9, September 1980. of Storm-Generated Currents," Journal of Geophysi­ cal Research, Vol. 79, No. 18, June 20, 1974. 6. Bea, R. G., "Updating of Height and Platform Resistance Descriptions Based on Preliminary Data 20. Forristall, G. z., Ward, E. G., Cardone, R.J. from Hurricane Carmen," CE-9 Report, Shell Oil and Borgman, L.E., "The Directional Spectra and Company, Report Released to API Task Force, Kinematics of Surface Gravity Waves in Tropical November 1974. Storm Delia," Journal of Physical Oceanography, Vol. 8, No. 5, American Meterological Society, 197 7. Bea, R. G. and Lai, N.W., "Hydrodynamic Loadings on Offshore Platforms," Proceedings, Tenth 21. Gade, H. G., "Effects of Nonrigid, Impermeable Offshore Technology Conference, OTC 3064, May 1978 Bottom on Plane Surface Waves in Shallow Water," Journal of Marine Research, 16(2), 1958. 8. Bea, R. G., Lai, N.W., and Moore, G. H., "Wave Forces on Shallow Water Platforms in the Gulf 22. Garrison, C. J., "A Review of Drag and Inertia of Mexico," Proposed for Publication· in the Forces on Circular Cylinders," Proceedings, Off-

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1982. Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 41. Jonsson, J.G., "Wave Boundary Layers and Fric­ 26. Hall, M. J., "Hurricane Generated Ocean Currents," tion Factors," Proceedings, lOth Coastal Engineer Proeceedings, Fourth Annual Offshore Technology ing Conference, American Society of Civil Conference, OTC 1518, 1972. Engineers, 1966.

27. Hamilton, R. C., "Storm Report of Hurricane 42. Lai, N. w., Bea, R. G., Niedoroda, A.W., and Edith, Sept. 16, 1981," Report by Baylor Company, Moore, G. H., "Gulf of Mexico Shallow Water prepared for participants of Gulf of Mexico Wave Heights," Proposed for Publication in Ocean Data Gathering Program, 1972. the Proceedings of the 1983 Offshore Technology Conference. 28. Hamilton, R. C., "Storm Report of , August 1-4, 1970," Report by Baylor 43. Lai, N. W., Niedoroda, A. W., and Bea, R. G., Company, prepared for participants of Gulf of "Assessment of the Morison Equation," Report Mexico Ocean Data Gathering Program, 1972. to Naval Facilities Engineering Command, Civil Engineering Laboratory, CR 80.022, July 1980. 29. Hamilton, R. C., "Storm Report of Hurricane Laurie, October, 1969," Report by Baylor Company, 44. Marshall, P. W. and Bea, R. G., "Failure Modes prepared for participants of Gulf of Mexico Ocean of Offshore Platforms," Behavior of Offshore Data Gathering Program, 1969. Structures, BOSS '76, Proceedings, Vol. 2, 1976.

30. Hamilton, R. C., "Storm Report of Hurricane 45. National Academy of Sciences, Committee on Camillie, August 17, 1969," Report by Baylor Offshore Energy Technology of the Marine Board, Company, prepared for participants of Gulf of Assembly of Engineering, National Research Mexico Ocean Data Gathering Program, 1969. Council, "Environmental Exposure and Design Criteria for Offshore Oil and Gas Structures," 31. Hamilton, R. C., and Ward, E. G., "Ocean Data May 1980. Gathering Program: Quality and Reduction of Data," Journal of Petroleum Technology, Trans. 46. Neumann, c. J., Cry, G. W., Caso, E. L. and AIME, 261, 1976. Jarvinen, B. R., "Tropical Cyclones of the North Atlantic Ocean, 1871-1977," National Climatic 32. Haring, R. E. and Heideman, J.C., "Gulf of Mexico Center, NOAA, 1978. Rare Wave Return Periods," Proceedings, Tenth Offshore Technology Conference, OTC 3220, 1978. 47. Nielson, P., "A Note on Wave Ripple Geometry," Proj. Rep. Institute of Hydrodynamics and 33. Haring, R. E., Olsen, O.A. and Johansson, P.I., Hydraulic Engineering, Technical University of "Total Wave Force and Moment vs. Design Practice," Denmark, No. 43, 1977. Proceedings, American Society of Civil Engineers, Civil Engineering in the Oceans IV, Vol. 2, 48. Nolte, K. G., and Hsu, F. H., "Wave Particle September 19791. Velocity Statistics in a Random Sea," Proceedings American Society of Civil Engineers Committee 34. Ho, F. P., Schwerdt, R. W. and Goodyear, H.V., on Reliability of Offshore Structures, Tucson, "Some Climatological Characteristics of Hurricanes Arizona, January 1979. and Tropical Storms, Gulf and East Coasts of the United States," NOAA Technical Report NWS 15, 49. Ohmart, R. D. and Gratz, R. L., "Drag Coefficients 1975. from Hurricane Wave Data," Proceedings, Civil Engineering in the Oceans IV, Vol. 2, 1979. 35. Hogben, N., "Wave Loads on Structures," Proceed- ings, 1nt'l. Conf. on the Behavior of Offshore SO. Ohmart, R. D., Gratz, R. L., and Malbry, G.O., Structures, Norwegian Institute of Technology, "Instrumentation Program for Evaluation of Vol. 1, pp. 187-219, 1976. Offshore Structure Design," Second Annual Offshore Tecynology Conference, OTC Paper 1264, 36. Hsiao, S. V. and Shemdin, "Bottom Dissipation in 1970. Finite-Depth Water Waves," Proc. Coastal Engineering Conference, pp. 435-448, 1978. 51. Pearcey, H. H. , Bishop, J. R. , "Wave Loads in the Drag and Drag/Inertia Regimes; Routes to 37. Hunt, J. N. and Brampton, A. H., "Effect of Design Data," Proceedings, Second International Fric.tion on Wave Shoaling," Journal of Geophysical Conference on the Behavior of Offshore Structures, Research, Vol. 77, pp. 6558-6564, 1972. Vol. 3, London, August 1979. 61 14 GULF OF MEXICO SHALLOW WATER WAVE HEIGHTS AND FORCES OTC 4586 52. Putnam, J .A., "Loss of Wave Energy Due to 59. Suhayda, J.N., "Surface Waves and Bottom Sedi­ Percolation in a Permeable Sea Bottom, " ment Response," Marine Gee-technology, Vol. 2, Transactions, American Geophysical Union, 30. 1977. p. 349-356, 1949. 60. Tubman, M.W. and Suhayda, N. J., "Wave Action 53. Riedel, H. P., Kamphuis, J. W. and Brebner, A., and Bottom Movements, in Fine Sediments," "Measurement of Bed Shear Stress Under Waves," Proceedings 15th Coastal Engineering Conference, Proceedings, 13th Coastal Engineering Conference, Vol. II, p. 1168-1183, 1976. American Society of Civil Engineers, 1972. 61. U.S. Army Coastal Engineering Research Center, 54. Sarpkaya, T., "In-Line and Transverse Forces "Shore Protection Manual, Vol. I," Dept. of on Smooth and Sand-Roughened Cylinders in Os­ the Army Corps of Engineers, 1977. cillatory Flow at High Reynolds Numbers," Report No. NPS 69SL76062, U.S. Naval Postgraduate 62. Vugts, J. H., "A Review of Hydrodynamic Loads Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 School, Monterey, California, June 1976. on Offshore Structures and Their Formulation," Proceedings, Second International Conference on 55. Schapery, R. A. and Dunlap, W. A. , "Prediction the Behavior of Offshore Structures, Vol. 3, of Storm-Induced Seabottom Movement and Platform London, August 1979. Forces," Tenth Annual Offshore Technology Conference, OTC 3259, 1978. 63. Ward, E. G., Borgman, L.E., and Cardone, V.J., "Statistics of Hurricane Waves in the Gulf of 56. Sheath, J.F.A., "Wave Induced Pressures in Beds Mexico," Tenth Offshore Technology of Sand," Proceedings, American Society of Conference, OTC 3229 1979. Civil Engineers, 96, HY2, 1970. 64. Wayde, B. G., and Dwyer, M., "On the Application 57. Shemdin, O.H., "Wind Generated Current and Phase of Morison's Equation to Fixed Offshore Plat­ Speed of Wind Waves, Journal of Physical forms," Proceedings, Offshore Technology Oceanography, Vol. 2, 1972. Conference, OTC 2723, 1976.

58. Standing, R. G. "Wave Loading on Offshore 65. Wilson, B. W., "Deep Water Wave Generation by Structures: A Review," National Maritime Moving Wind Systems," Journal of Waterways, Institute, Feltham, February 1981. Harbors and Coastal Engineering Division, American Society of Civil Engineers, Vol. 87, No. WW2, May, 1961.

62 TABLE 1 Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 TABLE 2 SUMMARY OF WAVE ATTENUATION CALIBRATION RESULTS SUMMARY OF WAVE CRITERIA (100-YEAR)

Representative ..~oproach ~lumber Offshore Hurricane Deep Water,Hindcast I Sediment Size (ft) •ater •1 #2 "3 Area Data H.(ft) , T(sec) Depth I Area I API l"c~o~an _jft) A I 3 I • fq_ef. !_~vel) f 0 •e-1982l

S. Padre Island no data :.ave Heignt ( f~) I 240 58 68 66 63 a 56.6 N. Padre Island no data 189 65 64 o2.5 65.0 55.7 6() ,, 12.0 4x1o-4 109 55 61.0 53.0 Mustang Island Allen '80 31 75 53 53 53 54.3 48.5 Matagorda Island no data Brazos no data Wave Feriod (secJI 240 (ll to ~5) 12.3 16.0 4x1o-4 189 12.3 Galveston Anita • 77 20 10.5 109 12.6 High Island Carla '61 26 11.0 4x1o-4 75 !2.2 Audrey '57 27 11.3 4x1o-4 ~ou; Tide ( f:) I 240 3.5 3.5 5. 7 11.3 4x1o-4 West Cameron Audrey '57 I 32 i39 3.7 3. 7 5.8 4x1o-4 East Cameron Camille '69 ' 13 12.4 109 4.8 4.8 7.2 Carla '61 34 11.0 4x10-4 75 6.3 6. 3 8.0 4x1o-4 Audrey '57 32 11.0 Corrent ( f':./sec) I 240 3.9-1.5 0 3.4-0.4 Vermi 1 ion Allen '80 22 11.2 4x10-4 189 3.4-2.0 0 3.2-0.4 Hilda '64 30 11.0 4x10-4 109 3.1-2.3 0 2.3-0.4 75 2.3-2.5 0 2.6-0.4 Audrey '57 32 10.0 4x1o-4 S. Marsh Island Allen '80 20 10.2 4x10-4 :;rag Coeff. I 240 0.6 0.6 0.65-0.75* 8.2 4xlQ-4 I 189 0.65-0. 75• Celia '70 18 109 Camille '69 17 12.5 4x1o-4 75 0.65-0. 75* Hilda '64 31 10.0 4x1o-4 10.0 10xlo-4 Inertial Coeff. I 240 1.5 1.5 l.l-2.0 Eugene Island Anita '77 20 189 1.4-2.0 Carmen '74 30 13.2 10xlo-4 109 Hilda '64 33 10.5 10xlo-4 75 1.4-2.0 9.6 10xlo-4 Audrey '57 28 ·~ar:.r.e ?'Jui hg Ship Shoal Carmen '74 33 12.2 lOxl0-4 ~ ~n. r'!C1a1 i Celia '70 16 7.7 10x1o-4 10x1Q-4 't'ia.;e -neory 240 Stokes Fi:'"h s_, •• , F'f:n I Stokes Fi'th Ccrnille '69 17 11.1 :S9 :tokes Fif:n St.JKe·s l:"i ftn 5:oi (1974) <( Ward et a/ (1978) 3: 50 and :!! Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 :::> Haring and Heideman :::i! 40 (1978) X <( :::i! 30 0 w 1- (.) w 20 a_ X w 10

0 Fig. 1-Probability distribution of hindcast expected maximum wave heights in deep water.

MISS ALA. FLA. LOUISIANA

D

.<11jlllllllllmLIIIIIIIIIIIIIIUJIII lllllolollllllllll!lllllllllllllll:t-U

I, III

1,1

Mustang Island Galveston H1gh Island West Cameron East Cameron Vermilion LEGEND South Marsh Island Eugene Island • Measured Data Ship Shoal • Inferred Data South Timbalier Grand Isle West Delta

Fig. 2-Subdivisions of continental shelf, wave attenuation paths, and locations of wave height data. 35 35 I I

30 I --+----'Cw.~==--- 30 TT {' .L South Marsh Island :::: :::: 25 ;-it 1- High Island 25 Ship Shoal :I: 1- ..- ~ (!) :I: L /

Tg /-T 1 Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 ~ w SM/6/ :I: w 20 :I: 20 ., III I w w t > > <{ ~ :;:: .,~l T f+..!. 1- 15 z 1- 15 I <{ z I u <{ j u I .1 G: G: z ' (!) 10 z (!) 10 .f (J) I (J) • Hurricane "Audrey" (1957) t Hurricane "Hilda" (1964)

5

WATER DEPTH, fl WATER DEPTH, fl A B

35 35

STI76 .I T -<. South Timbolier (_J.------West Delta ------30 30 -1 I STI62 I ...,...... - --~- I :::: ~/ I ' / ,., ... """" 25 J.-.1:"' ...... 25 I 1- tt / 1- :I: ST54 ------:I: ~ I --- ~ I w ST2/ w :I: 20 :I: 20 w ..J w Jl > > <{ <{ South Marsh Island :;:: !7 :;:: if 1- 15 1- J z z 15 <{ <{ u 1 u G: G: z 10 z ~ (!) 10 (J) (J) Hurricane "Carmen" (1974) Hurricane "Allen" (1980)

5

WATER DEPTH, ft WATER DEPTH, fl c D Fig. 3-Hindcast and measured wave heights, hurricanes Audrey {1957), Hilda {1964), Carmen (1974), and Allen (1980). Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 99.9 99.9 99.9

I 99 99 I 99 I I 98 98 I 98 I 95 95 I 95 VI 90 VI 90 I en en I en w 90 w w I :J :J :J 80 ....J ....J 80 ....J > > I/ u. u. u. I 0 I 0 0 I 60 w w 60 w (.') 60 I (.') (.') ::::: ::::: f- I I i= f- 5 • Area ::> ~. 5 / /95% Confidence u I u u I i Area 2 I 2 I 2 I I I I WATER DEPTH WATER DEPTH >150ft WATER DEPTH I I < 75ft 75 to 150ft

0.1 0.1 0.1 0.4 0.6 0.8 1.0 2.0 3.0 4.0 0:.4 0.6 0.8 1.0 20 3.0 4.0 0.4 0.6 08 1.0 20 3.0 4.0 H Measured H Measured H Measured Ratio= Ratio = Ratio = H Hindcast H Hindcast H H indcast A B c Fig. 4-Accuracy of hindcast wave heights in water depths greater than 150 ft., 75 to 150ft., and less than 75 ft. 75 T~

70 70

65 65 ;;: ;;: 1-- :r: 60 1-- 60 (!) :r: w ~ :r: UJ :r: UJ > 55 UJ 55 < > 3:: < 3:: X < 50 x 50 ::0 < ::0 100 Year Wave 100 Year Wave

45 11 45 Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 Region "A Region "s"

40 40 0 50 100 150 200 250 300 350 400 450 50 100 150 200 250 300 350 400 450 WATER DEPTH, It WATER DEPTH, It A B

75

70

65 ;;:

1-- :J: 60 (!) UJ :X:

UJ 55 > < 3::

X 50 < ::0 100 Year Wave 45 I Region .. c"

40 0 50 100 150 200 250 300 350 400 45( WATER DEPTH, It c Fig. 5-Hindcast tOO-year expected maximum wave heights in Regions A, B, and C.

ooco.-----~----.------r-----.-----.-----,

IOO·Yeor Conditions I 00 ·Year Conditions Reqion "A" RegiOn "A"

0000 .l...ll..U!.2.. ----- W1lh Cl~trtnl ----- w.lbouJ C111nnt

~ ...z w "0 •oo fooo " w "z .."'< : ~ ~ 1; " >coo ,( 400 ~

zooo '------'------_L_---..J....------'------'----" 0 100 200 300 zoo 300 WATER DEPTH , ft WATER DEPTH, fl A B Fig. 6-Variation of maximum base shear and mudline overturning moment with water depth, 100-year conditions, Region A, 8-pile platforms. 6000 .---,-----,-----,-----...,-----,-----,

IOO·Yeor Conditions 100 ·Year Conditions Regton "c" Regton "a" Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021

~

W'llvtPtr~od >000 >000 Vl'llhOI.IICurr•nt !S.c.),. ,, .. ~ ,," ~ a. 4000 t; a:: 4000 ,. <000 .. ~ iJi ~ ~ "' ~ ~ 3~00 !I x "' ~ "' , ... -- .... 2 -,,',, ~ ' ' "' ,, ,, ~ ' ', "' ~ 3000 "' 3000 ~:>:~~~ ------~~~-:~:)~- <·;~~:~~~~~~~~~~~;;;;~ "' '' I ' I ,/ ~ I 2:!!00 11 I I W1th Current 100 ·Year Condit tons ,' ~ Without Co.~rrtnl

zoooL---~--~---L--~--~--~ 2000·~-L-----L-----~--~~--~~--~ 300 0 100 zoo 300 wo 00

WATER DEPTH, ft WATER DEPTH, ft WATER DEPTH, ft

A A A

1000 .-----,----,------r----.----,...,.-----,

100 -Year 100 -Year Conditions Region Region "c" 000 T-'----.------,---,------,-----,-----,

000 ~ ~ --WdhCurrent .;; .;; ----- W•lhout Current ----- Wothout Current .. "!? 0 ' X I "2 / ... X ...z I > z ' ~ I I~ ~ ~ 600 ' 2 600 lit / ' :0 0 I It 2 I If / ,~:.> I If "' z I If "z ,' /1 " II' 'I' / ,~' ',,',, I /~I 1,,,,, I ,,';:,' /)1 i; ,;,," ! ~ 400 ~ 400 y'I Jjf"''" 2 X .,..I "' ~~ -.. "'~ :11/.// ... ;:.,~~ ~'/-,. .,., 1:;~~:/ __.,_, 200 ~~:,~:/ zooL-----~-----L-----L----~----~----~ 'ooL-----~-----L----~----~----~----~ 0 100 2:00 300 p 100 200 311l0 WATER OfPTH, It WATER DEPTH, fl . -WATER DEPTH • ft- - B B B FkJ. 7-Variation of maximum base shear and mudline Fig. a-Variation of maximum base shear and mudline Fig. 9-Comparisons of maximum base shears and mudline overturning moments with water depth, 1oo-year overturning moment with water depth, 1()()-year overturning moment with water depth, 1QO.year conditions, 8-pile platforms, Approach No. 1 (this conditions, Region B, 8-pile platforms. conditions, Region C, 8-pile platforms. study), No. 2 (API referooce level), and No. 3 (McMoRan pre-1982).