ML13309A838
| ML13309A838 | |
| Person / Time | |
|---|---|
| Site: | San Onofre  |
| Issue date: | 12/15/1980 |
| From: | Southern California Edison Co |
| To: | |
| Shared Package | |
| ML13302A500 | List:
|
| References | |
| NUDOCS 8103120698 | |
| Download: ML13309A838 (52) | |
Text
RECULAT YOCKET F-ilE C~OPY "WATERTIGHT RELIABILITY OF CONDENSATE -STORAGE TANK AND ITS CONCRETE ENCLOSURE WALLS UNDER OBE AND TORNADO EVENTS" ocket #P
,wsr Contirol #
Datee fDocumoflt R'EGUATORY 00OCKET FILE Revision 1 December 15, 1980 8103120698
Abstract The methodology and results of calculations are presented to demonstrate that the Condensate Storage Tank and its surrounding enclosure walls constitute a reliable storage facility to satisfy emergency cooling water requirements. The structural integrity, watertightness and water recovery aspects of the storage facility are verified with respect to the Category I Seismic event (DBE) and the Tornado event postulated for SONGS 2 & 3.
1.0 Introduction The SONGS 2 & 3 facility incorporates a condensate storage capacity of 650,000 gallons per Unit,. provided by two steel tanks (T-121 and T-120, Figure 1.1).
The Primary Condensate Storage Tank has a capacity of 150,000 gallons and is a seismic category I, tornado resistant facility.
The tank is fully capable of providing all the water required for a normal shutdown sequence. The second tank is a 50 foot diameter by 39 foot high conventional steel tank with a rated capacity of 500,000 gallons. This tank is enclosed in a concrete structure with a 4-foot thick base mat and 2 foot thick plane walls extending to a 30-foot height above the base, as illustrated in Figure 1.2 and 1.3.
According to the criteria dictated for the postulated emergency coolant requirement, 200,000 gallons of fresh water must be assured over a 24-hour period in addition to the 150,000 gallons currently provided by the Primary Condensate Storage Tank. These additional 200,000 gallons are expected to be provided by the existing Condensate Storage Tank and its enclosure structure subject to upgrading structural modifications to be defined herein.
A summary of the analytical results and design modifications that form the basis for the effectiveness of the water storage facility is presented next, and a more detailed description of the analytical procedures is covered in sections 2.0, 3.0, and 4.0.
1.1 Seismic Event
- 1.
The existing seismic class II tank is not adequate to withstand a seismic class I event. The salient findings are that the base anchorage of the tank is deficient, and that the lateral seismic response of the tank is high and subject to uncertain analytical determination because of the buckling mode of failure predicated for the thin vertical tank walls under high compressive stresses due to overturning moment. Therefore, (1) the base anchorage will be augumented by a new auxiliary concrete mat that interlocks the tank base with the surrounding walls and improves the uplift resistance at the tank base, and (2) a seismic restraint for the tank will be provided at the top of the walls in order to restrict the upper lateral response of the tank and preclude adverse interaction with the adjacent enclosure walls. (a) The "tight" restraint will eliminate the development of impact loads, and will deliver the lateral loads to the walls as "in plane" loads for efficient utilization of the ample shear wall load capacity.
- 2.
The foregoing measures, while definitely effective to restrict the seismic response of the tank and prevent damage to the sur rounding concrete structure, may not assure the watertight integrity of the tank. Therefore, the extreme case of total spillage of the tank water contents into the concrete enclosure will also be considered as a possible occurrence under a seismic event. In this case the concrete enclosure will be relied upon to retain the required water.
- 3.
Justification of the water-retaining ability of the concrete enclosure is based on (1) verification of its structural inte grity under the prescribed seismic event, and (2) evaluation of leakage rate resulting from concrete cracking due to maximum response and residual loading after the seismic event.
A structural analysis of walls by finite element modelling was performed considering hydrostatic loading, and the seismic inertia and hydrodynamic loadings derived from dynamic analyses.
- a.
The restraint would not be provided only if no adverse tank/wall interaction were to be demonstrated upon further non-linear rigorous analyses of the tank seismic response.
To obtain a bounded solution, the analysis was performed con sidering both the minimum and maximum water levels in the tank.
The maximum is considered to be.the full 500,000 gallon capacity of the tank while the minimum contents is 280,000 gallons, which will be enforced by plant technical operation specifications.
The results indicate that (1) the structural integrity of the walls as originally designed is adequate in both cases and (2) there are limited zones of high.flexural stresses with attendant concrete cracking.
The leakage calculation is based on the crack pattern evaluated under sustained hydrostatic loading taking into consideration the effects of the initial loading and the deformation undergone by the walls during maximum seismic response; see Figures 4.2, 4.3 and 4.4 for crack patterns. The corresponding calculated leakage proves to be insignificant and totally acceptable for both water levels as shown in Table 1.1.
The crack widths in zones below the top water level and above the base of the wall where a continuous waterstop is provided are smaller than the maximum 0.004 in. crack width recommended by the ACI(1) for water-retaining structures. The ACI criterion is referenced only for correlation and comparison of the order of magnitude of the calculated crack widths; it is not used as the basis for concluding that the structure is watertight. The most severe cracking results at the joint of the base mat with the wall where, in the case of maximum storage, the residual crack widths are substantially larger than the ACI recommended maximum width.
However, the condition is not adverse because (1) a flexible waterstop and shear key are provided at that joint as well as at all other joints, and (2) even if the leakage associated with the larger cracks is calculated considering the extreme case of a totally ineffective waterstop, the resultant leakage calculated would be acceptable, as summarized in Table 1.1.
1.2 Tornado Event
- 1.
The existing thin shelled tank is vulnerable to tornado missile perforation at the locations not shielded by the concrete enclosure walls. However, the adequacy of the tank is maintained based on consideration of (1) the governing missile trajectory and the angle of incidence dictated by the geometry of the tank with respect to the enclosure walls, and (2) the aggregate thickness of steel plate and travel through water that the missile must undergo before impacting the rearmost plate. These considerations demonstrate that the lower level of the tank corresponding to 220,000 gals. is not susceptible to perforation, see Figure 1.3. Therefore the minimum 200,000 gals. required plus the inside-tank unrecoverable allowance of 20,000 gals.
are retained as debris-free water inside the tank, and there is no need to rely on water in the annulus between the tank and its enclosure.
- 2.
The limited exposure of the steel tank above the enclosure walls renders the tank adequate for maximum positive wind pressure due to tornado event. The loading due to transient depressurization under tornado event will be reduced to an acceptable limit by incorporating venting modifications into the tank, thus rendering it adequate for all tornado pressure loadings.
04
Table 1.1 Leakage Evaluation (Gallons)
Initial Water Minimum Required Allowable Maximum Estimated Leakage Under Several Contents of plus Unrecoverable Water Postulated Cases, over the Prescribed Tank Water Leakage 24-Hour Period (A)
(B)
(A) -
(B)
Leakage Case 500,000 240,000 260,000 1,500 (1) Normal, credible case. Based on effective cracking counting (Maximum on the reliability of water specified stop and recognizing the high capacity quality class I concrete con of tank) struction which is physically evident from the completed structures.
40,000 (2) Same as (1), but considering the extreme of total failure of the waterstop at the loca tions of worst cracking at the base of all walls.
280,000 240,000 40,000 150 (4) Extreme case for low water level considering aggravated (Minimum water cracking due to seismic contents response and failed waterstop.
enforced by technical oper ation specifi cation)
2.0 Structural Evaluation and Analytical Model The structural analysis of the enclosure walls was performed with a finite element analytical model of the relevant portions of the structure as indicated in Figure 2.1. Wall (a) was emphasized analytically since its long horizontal span renders it as governing in terms of flexural response and crack formation. Wall (b) was also specifically analyzed and con sidered to be a conservative representation of the remaining walls which were not subject to specific analysis.
The boundary conditions were selected to obtain the most accurate eval uation of the displacement response undergone by the walls since it was recognized that flexural deflection and curvature are of vital importance in the calculation of crack widths. Accordingly, the rotational boundary condition at the vertical corners of walls (a) and (b) are appropriately represented by extending the model to include the connecting cross walls and introducing the fixed boundary at the far end of these walls.
(One edge of wall (b) is assumed fixed, with this fixity substantiated by the two cross walls (d) and (e) and the short span of wall (d)).
The base boundary condition of all walls was also considered fixed, which is sub stantiated by the 4 ft. thick base mat and its overburden load from the heavy tank contents.
Consistent with the necessity to obtain an accurate and conservative evaluation of the wall deformations, a relatively fine mesh of finite elements with reduced effective moments of inertia was adopted for the model. The element moments of inertia were reduced to recognize the flexural section that results upon concrete cracking, and were calculated in accordance with ACI Code 318-71, section 9.3.2.2. According to the Code formulation, the effective moment of inertia is a function of the actual flexural moment developed which in turn depends on the moment of inertia used. Therefore an iterative procedure was implemented and the ultimate result were deflections and curvatures which are conservatively higher than those initially obtained using the moment of inertia of the gross concrete section.
The foregoing considerations (boundary conditions, fine mesh and reduced moment of inertia), plus the proven reliability of plate finite elements used to analyze simple, flat wall structural systems, permitted a high confidence level in the stress analysis and evaluation of wall deformation.
The dominant structural behavior is two-way flexural action of the flat walls under pressure loading, with practically no tensile membrane behavior except for the slight horizontal tension developed at the walls' upper levels above the waterline. It follows that the load-induced concrete cracks of concern are dictated by the flexural behavior and corresponding curvature, both of which are highly predictable and accurately evaluated analytically.
The loadings considered were hydrostatic, and seismic loads due to inertial response of walls and hydrodynamic effects due to convective and impulsive fluid pressures derived per reference (2).
Three-component earthquake responses were considered, even though under the governing outward pressure loadings, there is no additive effect for the two horizontal components since the maximum out-of-plane displacement response of a single wall, at a given time, is the governing response. The hydrodynamic pressures from the earthquake components were combined by the SRSS. The resultant hydro dynamic pressure was combined with the seismic response of the walls by absolute summation as a conservative recognition of the long-period, "sustained" type of response characteristic of seismic sloshing of liquids.
3.0 Determination of Crack Widths The crack widths were evaluated using two different approaches, and the higher of the calculated values derived from the more rigorous approach was used in the leakage calculation.
In the first approach, the crack width is formulated as a function of the tensile stress in the reinforcing steel using an equation derived from experimental correlations. The formulation used is per ACI Committee 224(,
which in turn is an adaptation of the original research by Nawy(3)
&(4)*
The total crack width as obtained from the dominant flexural and the lesser axial tension stresses was calculated. The flexural stresses were determined by linear elastic analysis of the reinforced concrete section using working stress design (WSD) formulations. This is a conservative evaluation for sections subject to moments below the ultimate capacity, whereas for sections at or near the ultimate yielding moment, the appro priate ultimate strength design (USD) formulations were used. Axial stresses were found to be generally insignificant since the in-plane membrane tensions developed in this type of flat-wall flexural systems are normally low. The only locations with some axial tension were toward the top of the walls where horizontal tension related to a slight "hoop" action results, and the stresses were simply calculated as the tension load divided over the total area of horizontal reinforcing (< 1 ksi).
It is recognized that the stress dependent formulations for crack width are approximate and appropriate mainly for an evaluation of cracks by comparison of calculated values against maximum crack widths recommended in ACI 224 for various types of structures. For water retaining structures, a maximum crack width of 0.004 in. is recommended. This limit is basically satisfied by the crack widths calculated by the stress dependent formula tion under the sustained hydrostatic loading throughout the walls.
The only instances where the maximum width is exceeded are inconsequential because they are at locations above the water level, and at the base of the walls where a continuous waterstop is provided. Therefore, the stress-dependent
evaluation of cracks indicates a watertight condition, but it is recognized that the calculation is approximate and that a more direct verification of watertightness addressing the leakage derived from a more rigorous evaluation of cracks is necessary to establish a definite conclusion. The results of this analysis are provided in Section 4.0.
The second approach for the calculation of crack widths is based on the curvature or rotational deformation undergone by the flexural elements.
The basic postulation is that the rotational deformation, which is highly predictable and well defined by the flexural action undergone by the walls, is totally achieved through a concentrated rotation assigned to be effected at the postulated crack. This is a conservative assumption since it amounts to a total neglect of the actual flexural flexibility within the elements, and it implies the extreme of a series of rigid elements that attain the out-of-plane slab deflection by means of exaggerated rotations restricted to the postulated crack locations. The crack width then follows from the product of the rotation times the radius to the center of rotation which corresponds to the neutral axis of the section.
The approach is schematically represented in Figure 3.1, and is further described in the sample calculation per Appendix A. The resultant crack calculation is thus a reliable evaluation based on the fulfillment of compatibility with the analytically well defined flexural deformation of walls under pressure loading.
The crack widths calculated from rotational deformation are typically higher than those obtained per the stress-dependent formulation, and the final value is adjusted upwards by adding the axial tension component as previously calculated from the stress dependent formulation.
The most severe cracking develops at the base of the walls. At this location a single concentrated crack is a credible occurrence because of the pre-existing "cold" construction joint which, on the other hand, is appropriately safeguarded by a flexible waterstop. The flexible waterstop used is a proven product that has an excellent performance record during the many years of service in the industry. In the case under consideration, the watertight reliability of the waterstop is more decisively established upon considering the favorable confined and anchored conditions afforded to the waterstop by the reinforcing bars across the joint and the shear key provided. In addition, the reliability of waterstops subject to a much more severe function involving high differential motion across a wide 3-1/2 inch separation between two bodies of concrete has been reported favorably in reference (5).
REFERENCES (1) Control of Cracking in Concrete Structures, reported by ACI Committee 224.
(2) "Nuclear Reactors and Earthquake" TID 7024 U.S. Atomic Energy Commission, August 1963.
(3) Nawy, E.G., "Crack Control Through Reinforcement Distribution in Two-Way Acting Slabs and Plates", ACI Journal, Proceedings, V. 69, No. 4, April 1972.
(4) Nawy, E. G., "Crack Control, Serviceability, and Limit Design of Two-Way Action Slabs and Plates", Engineering Research Bulletin No. 53, Rutgers University, 1972.
(5) Report of Test on Seismic Vibration and Water Leakage Test on Rubber Waterstops for use in, Concrete Joint Systems, for W. R. Grace by Acton Testing Corporation, February 1974.
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4.0 Technical Approach and Basis for Leakage Analysis The leakage calculation is based on theoretical expressions for flow through parallel plates extended to model flow through cracks in the reinforced concrete walls.
A sunrnary of the deriviation of the equations is outlined on Table 4.1.
The application of equation (7) of Table 4.1 requires that the actual crack pattern be represented by horizontal cracks.
- However, the actual cracks are of conplex cross section and of variable aperture, there fore, equivalent constant apertures of cracks are calculated by the relation ships sunmarized on Table 4.2.(4) and Appendix B.
The vertical cracks were nodeled as equally dimensioned horizontal cracks at elevations 16.7, 11, and 6.2 ft.
For example, as shown on Fig. 4-1 the 5.8 ft.
segment of each vertical crack from the water surface (elevation 22.5 ft.) to elevation 16.7 ft. was taken as a 5.8 ft. long horizontal crack at elevation 16.7 ft.
Similarly, the segment of each vertical crack between elevation 16.7 and 11 ft. was taken as a 5.7 ft. long crack at elevation 11 ft., etc.
By consider ing the equivalent horizontal cracks as located at the lowest level of each vertical segment larger applicable heads result, and a onservatively larger flow quantity is thereby calculated.
Use of this conservative procedure considerably sinplified the calculations while maintaining the conservatism.
The leakage in the room can then be calculated in increments using equation (7) of Table 4.1.
4.1 Discussion of the Basis of and Conservatisms Inherent to the Equation Used to Estimate Leakage The parallel plate nodel for crack flow has been applied by various researchers in the petroleum and water resources fields since the 1950's.
A demnstration of the validity of the theory for laminar flow in both snooth-and rough-walled plates may be found, for example, in the work of Huitt (1),
who showed that such flow obeys Darcy' s law for low Reynolds (3) numbers.
This work was anplified and extended by Louis who experi mented on a wider range of surface roughness and flow rates, and produced a set of enpirical equations for snooth-and rough-walled cracks under both turbulent and laminar flow.
Louis' equations for snooth-walled and laminar flow are the same as those used in deriving equation (7).
His equation for rough walled cracks is a function of the relative roughness Kr = E/2b, where E is defined as the depth of surface roughness (measured peak to trough), and b is the ncxinal crack aperture.
If the crack exhibits surface roughness, the snoth-walled flow rate for a given gradient is reduced by nultiplying by the factor 1/(1 + 8.8 Kr. 5 ).
As an example, cracks with surface roughness equal to 20 percent of aperture, a value generally exceeded in concrete flexural cracks, would conduct approximately 22 percent less flow than snooth cracks.
The calculated leakage determined herein is thus conservative since surface roughness effects were not considered.
Another factor which conservatively is not considered in the idealization to parallel plate flow is tortuosity, as it affects crack length.
Flow rate for a given gradient is inversely prcportional to crack length through the wall, thus the effect of crack tortuosity is to increase the actual length of the flow path and decrease the flow rate.
The assump tion of laminar flow is also conservative because the flow rate varies directly with the change in gradient, whereas under turbulent conditions, the flow rate varies approximately with the square root of the gradient.
Fran the above conditions, it can be concluded that the use of a laminar snooth-walled parallel plate flow nodel for cracks will tend to over estimate the true flow rate which would occur in non-ideal rough-walled, tortuous fractures which may, in fact, experience turbulent flow.
Therefore, the use of equatin (7) will yield conservative estimates of flow through cracks in the reinforced concrete walls.
4.2 Case Studies The results of the analysis of the distribution of cracks and maxinum crack cpenings are shcwn on Figures 4.2, 4.3 and 4.4.
Specifically, Figure 4.2 shows the maximin crack pattern in the nost critical wall due to water and seismic induced loadings for the condition of the con crete enclosure containing 500,000 gallons of water, and Figure 4.3 shows the corresponding crack pattern for 280,000 gallons of water in the enclosure.
The crack pattern for the other three walls was calculated to be as shcwn on Figure 4.4 for the 500,000 gallon case.
Equation (7) of Table 4.1 was used to estinate leakage through the cracks.
All cracks were assumed to have a cross-sectional configuration defined by the naximum aperture at the inside or outside face of the wall as defined on Figure 4.2 and 4.3, and to have a uniform reducticn over a length of about 18 inches to a mininum aperture of 0.001 inches.
This minimum aperture is constant over the last six inches of wall.
In the case where the aperture at the inside face of the wall was less than.001 inches, a constant aperture equal to the aperture at the inside face of the wall was assumed.
Equivalent uniform apertures were calculated for each crack using the relationships shown on Table 4.2.
Vertical cracks were char acterized in a conservative nanner by three equivalent horizontal cracks at elevations 16.7, 11, and 6.2 ft. as described above and on Fig.
4.1.
The most severe crack octurs at the base of the wall where imposed seismic and hydrodynamic nonents are the greatest.
Figure 4.5 shows the nost conservative interpretation of this crack consi.dering the maximurn apertures at the inside and outside faces of the wall simul taneously.
The maxinum crack aperture of 0.039 inches is shcwn on the inside face of the wall, and it decreases uniformly to a minimum aperture of.023 inches at the outside face of the wall.
Because of the gecmetry of the shear key, a minimm aperture of.008 and 0.007 inches occur at segments BC and ED of the crack as shcwn in Figure 4.5.
In this respect it is noted that the effect of the outward hydrostatic loading imposed by the spilled total contents of the tank is to enlarge the crack aperture on the inside face of the walls and to reduce the aperture on the outside face.
For this analysis a conservative conbina
- ticn of apertures was selected. wherein the maximum hydrostatic loadings were considered in calculating the enlarged inside aperture but were disregarded in reducing the outside aperture.
The maxium crack apertures shown on Figures 4.3, 4.4, and 4.5 were developed from the governing crack analysis. described above.
The minirmum aperture of.001 inches for all cracks (except for the foregoing conserrvative interpretation for the base crack in the wall shown on Figures 4.2 and 4.5) was developed considering the 250 to 500 psi range of noral ccnpressive stress calculated at the various sections from the flexural ronent obtained under the sustained hydrostatic load as pre sented in Appendix A.
The stress is relevant to evaluate the minimum crack aperture at locations where the linear behavior prevails and the flexural compression zone may experience prior cracking due to moment reversal caused by the lateral seismic inertial load fran the walls.
The effect of this normal compressive stress is to induce contact and closure of the crack, which in turn tends to decrease the flow rate.
The effect has been evaluated from laboratory tests performed on cracks in various natural materials.
Work perfored by Iwai(2) on basalt, granite and marble is used as described in Appendix C to develop the effect of stress on crack aperture as shown on Figure 4.6.
Though no data are available for concrete, the granite and marble data approximate concrete as the concrete is otposed of granitic aggregate in a linestone matrix similar to marble.
It is expected that variations in this data would be minimal for concrete and the leakage results would be well bounded by the conservative assurrption of the lower crack dimension in Figure 4.5.
An aperture of.001 inches represents a conservative interpretation of the referenced test data.
In the case where leakage was calculated across the specific crack shown in Figure 4.5, the presence of the water stop was neglected as were the waterproofing comtpound between the inside wall face and the new top mat slab.
The presence of the new concrete mat itself, which will be placed to improve seismic anchorage of the base of the tank, was also neglected for conservatism.
Specific cases included in the analyses were:
- 1.
the raxinum crack pattern with no leakage through the bottan crack due to the presence of the water stop for an initial volume of 500,000 gallons of water (Figure 4.2);
- 2.
the same as case 1 but conservatively neglecting the water stup throughout the total crack length and assuming leakage through the bottan crack on the vertical wall characterized on Figure 4.2 excluding the cracks identified by asterisks.
These crack widths become.001 inches upon consideration of closure due to hydro static loading.
Case 5 describes the conservative case where hydrostatic closure was neglected.
- 3.
the maxinum crack pattern with no leakage through the botton crack due to the presence of the water stcp for an initial volume of 280,000 gallons of water (Figure 4.3);
- 4.
the sane as case 3 but neglecting the water stcp and assuming leakage through the botton crack;
- 5.
the same as case 1 but neglecting the water stcp in the critical wall and assuming the most critical canbination of apertures as indicated by the table in Figure 4.5; and
- 6.
additional leakage obtained from permeable flow through sound concrete.
For all the above cases except cases 5 and 6, the crack pattern in.
the nost critical wall was conservatively assumed to occur in all four walls by multiplying the leakage for the nost critical wall (Figures 4.2 and 4.3) by a factor of 4.
Under case 6 the seepage due to the perme ability of uncracked concrete was considered.
The permeability coeffi cient was determined per references (5) and (6) based on the maximum aggregate size of 1-1/2 inch and the favorably low water/cement ratio of 0.57 corresponding to the concrete mix (with 10% pozzolan) used in the enclosure structure.
The total surface area of the walls and base mat was considered, and conservatively, all were subject to the maxinuma head of 22.5 feet of water.
At the request of the NRC staff a seventh case was also evaluated to determine how large a localized aperture at the bottom of the wall would have to be to discharge the 260,000 gallons of excess water not required for cooling over the 24 hour2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> period upon starting with the 500,000 gallon initial volume case.
The naxinum length of opening was assumed to be equal to the reinforcing bar spacing (1-ft) because the reinforcing steel would restrain a localized opening due to its tensile capacity.
With this restraint in effect, the mininum aperture of the bettan crack was back calculated such that 260,000 gallons of water would be discharged in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
In the interest of conservatism all calcula tions were made assuming no reductions in head due to intentional draw down for cooling water.
4.3 Results of Analyses The calculated leakage for cases 1 and 2 defined above was less than 1500 and 3000 gallons in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />, respectively.
The corresponding leakage for cases 3 and 4 was less than 150 gallons for either case.
For case 5, less than 40,000 gallons of leakage in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> is calculated.
A sunrnary of the results of these first five cases is presented on Table 4.3 along with a schematic description of the gecrnetry of the base crack for each case.
For case 6 the calculated leakage is insignificant anounting to 1.5 gallons over the 24 hour2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> period.
For the localized 1/2 to 1-foot long crack at the bottn of the wall the average aperture through the wall required to casue 260,000 gallons of leakage in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> was calculated to be about.05 to.08 inches.
This is almost two orders of nagnitude greater than the conservative.001-inch minimum aperture of nost of the crack and about cne order of nagnitude greater than the mininum aperture of the base crack (where the water stop is effective) of the nost critical wall characterized on Figure 4.2.
If the reduction in head resulting from the intentional drawdown of the water in the room is incorporated in this last extreme analysis of a localized opening, an additional 80,000 to 100,000 gallons of water would renin in the rocrn at the end of 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> (i.e., 80,000 to 100,000 gallons less leakage fran cracks would occur).
In summary, the Applicant estimates that less than 1500 gallons of water would leak through the Condensate Storage Building walls in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> under the worst loading conditions (i.e., high water level due to 500,000 gallons of water with DBE loadingO.
By neglecting the effectiveness of the water stcp throughout the length of the base crack in the nost critical wall the resulting leakage would still be less than 3000 gallons which is less than 2% of the excess 260,000 gallons of water available for cooling for that period.
Assuming the nost critical conrbination of apertures as indicated in the table on Figure 4.5 (a condition that is not credible because the naximum aperture on the outside face neglects the hydrostatic head but represents an extreme limiting calculation) leakage would be less than 40,000 gallons in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
Further, the Applicant calculates that a local aperture of a crack restrained in length by the reinforcing bar spacing could be almost two orders of magnitude greater than the conser vative.001 inch opening at the outside face of the wall and still leave almost 100,000 gallons of excess water in the room after 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
REFERENCES (1) Huitt, J. L., "Fluid flow in simulated fractures," AICHE Journal, v.
2, p. 259, 1956.
(2) Iwai, K., "Fundamental studies of fluid flow through a single fracture," Ph. D. thesis, University of California, Berkeley, 208 p., 1976.
(3) Louis, C., "Stromungsvorgange in Kluftigen Medien and ihre Wirkung auf die Standischerheit von Bauwerken und Boschungen im Fells,"
Dissertation Universitat (TH) Karsruhe, 1967. Also.published in English as:
"A study of groundwater flow in jointed rock and its influence on the stability of rock masses,"
Imperial College Rock Mechanics Research Report No. 10, September 1969.
(4) Wilson, C. R., and Witherspoon, P. A., "An investigation of laminar flow in fractured porous rocks," Department of Civil Enginering Publication 70-6, University of California, Berkeley, 1970.
(5) Concrete Manual. A water resources technical publication, U.S. Depart ment of the Interior, Bureau of Reclamation. Eighth Edition, 1975;'
Figure 17.
(6) Mass Concrete for Dams and Other Massive Structures, reported by ACI Committee 207; Table 3.5.1.
Table 4.1
SUMMARY
DEVIATION OF LEAKAGE EQUATIONS
-Wall A = Area of Room
-- T i=n bi = Aperture of Crack i Li = Length of Crack i i
ip
= Mass Density of Water g = Acceleration due to Gravity Crack i=1 p = Viscosity of Water.
w = Width of Wall h = Height of Water in Room line no FLOW RATE:
Q
=
K i
A' (1)
Hydraulic Gradient Flow Area Conductivity USING THE PARALLEL Adh b pg-)
(bL)
(2)
PLATE MODEL dt 12,u w
(HUITT 1956)
-nn dh pg b-L n
pg b-3 L
FOR n CRACKS:
A j
g
-]
h (t(3) dt
.12 12 w
P9 b-3 L-n let C-and Cn
LCi (4) i
1 ISOLATING CONSTANTS n
also Mi =C hi and Mn
=
M (5)
AND SIMPLIFYING:
A
=
Cnh -
Mn]
(6)
UPON INTEGRATION:
In tt -_
t-(7)
Cn In ho-Mnt
Table 4.2 CALCULATION OF EQUIVALENT APERTURES Wedge shaped cracks:
b1 >b 2 q
by w
W b2 b eff = 2bl 2 b2 2
or b1 + b2 q
b2 b1 (Appendix B, Reference B-1)
Cracks in series:
wi + w 2 b3 eff =
W1 W2 bb 2
b1 b2 w1 (Appendix B, Reference B-1)
Cracks in parallel:
bWeff
=
.L1 b 13 + L2 b2 3
q L1 L2 (Appendix B)
Table 4.3
SUMMARY
OF RESULTS OF ANALYSES FOR CASES 1 THROUGH 5 CASE DESCRIPTION RESULTING ESTIMATED LEAKAGE GEOMETRY OF BASE CRACK
- M 1
Crack pattern shown on Figure 4.2 on all walls
<1,500 gallons in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> with no leakage along the dashed crack where
.001 3
the water stop is effective. (Actual crack con figuration for 500,000 gallon tank volume) 2 Same as Case 1 except that leakage is assumed
<3,000 gallons in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> from the dashed crack on Figure 4.2 (neglect water stop) on all walls. This is conservative
.0011
.039" in that the water stop is neglected and the largest crack from the wall with the longest span is assumed for all walls.
3 Crack pattern shown on Figure 4.3 on all
<150 gallons in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> walls with no leakage along the dashed crack
.oo1' 0o122 where the water stop is effective. (Actual crack configuration for 280,000 gallon tank volume.)
4 Same as Case 3 except the dashed crack on
<150 gallons in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> Figure 4.3 leaks (neglect water stop) on all
.001oo walls.
5 Same as Case 1 except assume the dashed
-40,000 gallons in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> crack on Figure 4.2 on one wall exhibits the See Figure 4.5 most conservative combination of apertures as shown on Figure 4.5.
- Solid water stop indicates that it is effective to stop leakage.
Dashed water stop indicates that it was neglected in leakage calculation.
30'
/Water Table at el. 22.5' 20' c c 2
C3 C4 C5 C6 C7 C8 Cg c 1 0 C1 1 C 1 2 C1 3 c4 El. 16.7 C
cl + C2 +c 3 +.......14 El. 16.7 b2 k-Equivalent horizontal crack C b
b b
b3 b4 b5 b6 b7 b8 b
b0 b11 bl2 El. 11
~B
- bi + b2 + b3 +..........
bl4 E.1 EI. 11 Bb+
+b+El.
11
- 10. -Equivalent horizontal crack B al a2 EI. 5.7 A
a, + a2 El. 5.7 Equivalent horizontal crack A 0*
I I
I I
0' 10' 20' 30' 40' 50' 57.5' Figure 4.1 EXAMPLE OF MODELING VERTICAL CRACKS BY EQUIVALENT HORIZONTAL CRACKS
30.0' CV) l Iq CV)
C V)C%
27.5'o a
0 0
0 0
0 0
0 00 25.0' 8
22.5' 00 EL.
20.0 c8 8z85 22.5' 17.5' 15.0' 12.5' v
10.0' 7.5' 5.0'
.0014
.0033
.005 0054
.005
-0033
.0020
.0010 2.5'
.0019
.0058 0090.094 Z-3 L
.03
.. 3 J)790019
.0'
(.0087)
(.020)-
(.023)*
(.020)*
(.0087)*
Figure 4.2 CONDENSATE STORAGE TANK AREA WALL-1 DIAGRAM SHOWING CRACK APERTURES IN INCHES Crack apertures shown relate to maximum aperture on inside wall face.
Crack apertures shown in parenthesis indicate maximum aperture on outside wall face.
Bottom crack shown by a dashed line contains the water stop.
- These apertures occur only with no hydrostatic pressures on the wall; therefore the combination of apertures shown is the most conservative combination.
2.5' 5.0 7.5'.
I 7.5' I
10.0' 12.5'
-n. 15.0' M
17.5' n
20.0' I
e
= Z 22.5' oI
- 25.
CD m275
~a I
O 25.0' I
o.L C-I
)m 27.5'
-r CA>
CD I4 3
CIL S32.5'.
I A
30.0' r-m> >
CDO
~ > 37.5"'
_m 50..9 0
4u m 32.5'
-c >
45.0' 47.5' 5L 0.0',
52.5' 55.0' 57.5'
.0047
.0048
.00606 2.5'
.00399
.00451
.00463 5.0' 7.5' 10.0' 2.5'2 a
(.0016)
.0011 3
o0 15.0'
(.0012)
(.0022)
.0017 CA 17.5' 0 o 0
'z
(.00203)
(.0030)
.0031 0
20.0' 0
a
(.00208)
(.0032)
.0034
<T.
z>
22.5' Sm m
j
(.00206)
(.0033)
.0035 25.0'
(.00203)
(.0034)
.0034
=.33 27.5'
. 3 m m
(.0020)
(.0030)
.0026 o 3w m 30.0' 3
(.0019)
(.0025)
.0031 z
Cm 32.5' R
,+MC n>
l(.00221)
.0017 m
35.0' 0~
IA I>
37.5' 0
c I
40.0' CDa
.D 42.5'
.0040
.0045
.0046 45.0'
.0047
.0048
.0061 47.5' m0
240D FACE OF WALL CONSERVATIVE COMBINATION OF MAXIMUM CRACK APERTURES Segment Max. Aperture (inches)
Segment Length (inches)
A to B 0.039 to 0.034 7.63 B to C Uniform 0.008 1.55 C to D 0.034 to 0.028 8
D to E Uniform 0.007 1.55 COMPON COMPOUND E to F 0.028 to 0.023 7.63 REINFORCING BAR AREINFORCING BAR OUTSIDE RENORIG A FACE OF WALL 1
w z
,---WATER STOP A
4 SHEAR KEY 4
1 1
3 D
C SCALE 1"= 3" Figure 4.5 SECTION THROUGH BASE OF WALL
4 3
2 I
- 1 O
500 1000 1500 2000 2500 COMPRESSIVE AXIAL STRESS (psi)
Figure 4.6 EFFECT OF COMPRESSIVE STRESS ON APERTURE
A 0
Appendix A 0
0
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Appendix B.
Backup for Table 4.2 The equaticm for wedge shape fracture is discussed on pages 60 and 61 of the attached Wilson and Witherspoon (1970) paper attached as reference B-1 which references experiemental verification by Lcmize (1951).
The equation for cracks in series are developed theoretically in Wilson and Witherspoon (1970) on pages 57 through 60 and checked for consistency with Laniize (1951) experimental work on wedge shaped cracks.
(Note that equation 11-28 is identical to the appropriate equation in Table 4.2 except that crack length is designated by "1" in equation 11-28 and by "W" in Table 4.2).
The equation for cracks in parallel is simply a weighted average on b3 for which there is anple experimental verification that flow is prporticnal to b3 as discussed in Witherspoon et al.
(October 1979) attached.