off the seafloor was accurate. In Refer- 

 ence 1 concern was expressed that the 

 original number of links off the seafloor 

 could be in error by ±1.5 links (equivalent 

 to 0.73 cu ft or 21 liters). With the data 

 from Sphere no. 12, it is now known that 

 that error estimate was too high. A new 

 estimate of error is +0.5 link (0.2^ cu ft 

 or 7 liters), which is also the error 

 estimate between different inspections. 



Figure 2^ shows the relationship 

 between total water intake and time in 

 the ocean for all of the spheres (except 

 Spheres no. 17 and 18, which were half 

 coated) where chain link count data were 

 obtained. The coated spheres do not show 

 any evidence of having permeated water. 

 This case is known to be true for Spheres 

 no. 11 and 13. The coated spheres range 

 in depth from 2,440 to 4,875 feet (744 to 

 1,486 m). 



The waterproof coating appeared 

 quite effective. This was an unanticipa- 

 ted finding, because the coating was not 

 a complete barrier. Pin-holes or "fish- 

 eye" openings existed in the coating. The 

 coating also bridged air pockets in the 

 wall near the surface; these locations 

 had the coating broken because the 

 water pressure pushed the coating into 

 the air pocket. Water definitely had 

 access to the concrete wall through 

 these openings. 



When a hole was drilled in the walls 

 of Spheres no. 11 and 13, the concrete 

 was found to be quite dry in appearance. 

 It is apparent that the pin-hole openings 

 became watertight with time. Continued 

 hydration of cement, microorganisms, 

 and chemical changes were probably 

 some of the causes for the concrete 

 becoming watertight. Whatever the 

 mechanism, it can be speculated that it 

 was functioning in the uncoated concrete 



too. From Figure 24, it is shown that, in 

 general, the uncoated concrete spheres 

 became watertight- In less than 1 year, 

 the uncoated spheres absorbed (and 

 permeated) water at a faster rate than 

 the coated spheres. However, after 1 

 year the additional water intake was 

 quite small. 



One method of analyzing permeabil- 

 ity results is to apply D'Arcy's viscous 

 flow equation. For a sphere, this 

 equation can be expressed as:* 



Q t 



T A h ^^' 



s 



where K = permeability coefficient, 

 ft/sec (m/sec) 



Q = quantity of permeated 

 P seawater, ft-^ (m-^) 



T = time (sec) 



t = wall thickness, ft (m) 



A = interior surface area, 

 ' ft2 (m2) 



h = pressure head, ft (m) 



D'Arcy's theory assumes K^^ to be 

 constant with time. However, the 

 permeability results from the spheres 

 show that Kc decreases with time. To 

 account for the change in rate of Kq, a 

 secant K^ is utilized. This is analogous 

 to the secant modulus of elasticity for 

 nonlinear materials such as concrete. 



In Figure 25 the secant K^ values 

 are shown as a function of time in the 

 ocean. Data from two spheres tested in a 

 pressure vessel for up to 42 days are 

 included. These spheres were similar to 

 the ones in the ocean. It is interesting 



*This expression is different from that given in References 1 and 5 because 

 As is now defined as the interior surface area and not as mentioned previously 

 as the exterior surface area. This revised equation will give K^ values 30.6% 

 greater than the previous equation. 



31 



