ML20132G824
| ML20132G824 | |
| Person / Time | |
|---|---|
| Site: | Waterford  |
| Issue date: | 06/21/1984 |
| From: | BROOKHAVEN NATIONAL LABORATORY |
| To: | |
| Shared Package | |
| ML17198A272 | List:
|
| References | |
| RTR-NUREG-0787, RTR-NUREG-787 NUDOCS 8510010634 | |
| Download: ML20132G824 (34) | |
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l REVIEW 0F WATERFORD III BASEMAT ANALYSIS Structural Analysis Division Department of Nuclear Energy Brookhaven National Laboratory Upton, NY 11973 June 21,1984 s
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8510010634 840621 PDR ADOCK 05000382 E PDR 9
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1.
. TABLE OF CONTENTS Page No.
INTRODUCTION . . . . . . . . . . . . . . . . . ................................ 1
=.
GENERAL COMMENT
S . . . . . . . . . . . . . ................................ 2 STRUCTURAL ANALYSIS TOPIC REVIEWED ........................... 3
- 1. Dead Loads (D) . . . . . . ................................ 3
- 2. Buoyancy Forces (B) . ................................ 7 ,
- 3. Variable Springs Used For the Foundation Modulus .... 7
- 4. Vertical Earthquake Ef fects ......................... 8
- 5. Side Soil Pressure . . ................................ 8
. 6. Bounda ry Constraints ................................ 10
- 7. Finite Element Mesh and Its Effect .................. 10
- 8. BNL Check Calculations ............................... 11 CONCLUSIONS AND RECOMMENDATIONS .............................. 13 AP PE NDIX A LIST OF CONTRIBUTORS ............................. A-1 AP PE NDIX B STRESSES INDUCED WHILE POURING BLDCKS ............ B-1 APPENDIX C EFFECT OF SIDEWALL LOADS ON BASO9AT CAPACITY ..... C-1 6
O D
9
INTRUDUOTION __
At ..t he request of SGEB/NRR, the Structural Analysis Division of the Department of Nuclear Energy at BNL undertook a review and evaluation of the HEA Waterford III mat analysis documented in Harstead Engineering Associates (HEA) Reports, Nos. 8304-1 and 8304-2. Both reports are entitled, " Analysis of Cracks and Water Seepage in Foundation Mat". Report 8304-1 is dated September 19, 1983, while Report 8304-2 is dated October 12, 1983. Major topics addressed in the first report are:
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3 (1)' Engineering criteria used in the design, site preparation and con-struction of the Nuclear Power Island Structure basemat.
(2) Discussion of cracking and leakage in the basemat.
(3) Laboratory tests on basemat water and leakage samples.
(4) ' Stability calculations for the containment structure.
The second report concentrates on the finite element analysis and its results.
Specifical.ly, it describes:
(1) The geometric criteria and finite element idealization.
(2) The magnitude and distribution of the loads.
(3) The final computer results in terms of moments and shear versus the resistance capacity of the mat structure.
Supplemental information to these reports were obtained at meetings held in Bethesda, MD, on March 21 and 26, 1984, at the Waterford Plant site in Louisiana on March 27, 1984, and at Ebasco headquarters in New York City on April 4,1984. At the close of the EBASCO meeting, a complete listing of the HEA computer run was made available to BNL.
The BNL ef forts were concentrated on the review of the results presented in report no. 8302-2 and on the supplemental information contained in the com-puter run given to us by HEA. This computer run contains 9 load cases and their various combinations. The input / output printout alone consists of
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roughly two thousand pages of information. Selected porti'ons wer'e' reviewed in detail, while the remaining sections were reviewed in lesser detail. C om-ments regarding the reviewed work ~ are given in the sections that follow.
GEriERAL COMMENTS :
Basically, the HEA report concludes that large primary moments will pro-duce tension on the bottom surface of the mat. For this condition, it is shown that the design is conservative. Furthermore, the shear capacity vs.
the shear proauced by load combinations are concluded to be adequate although a few elements were found to be close to the design capacity. Accordi ngly, the cracking of the top surface is attributed only to " benign" causes such as shrinkage, differential soil settlement, and temperature changes.
Based on the discussions held with EBASCO and HEA, and on the review of data given to BNL, it is our judgement that the bottom reinforcement as well as the mat shear capacity is adequate. The statenent that the cracking of the top surf ace is attributable to " benign" causes however has not been analyti-cally demonstrated by HEA. In the BNL review of the reports and data, an at I
tempt was made to ascertain the reasons for the existing crack patterns that appear around tne outside of the reactor shield building as depicted in Figure U-1 Appendix U of the HEA Report 8304-2. Other effects influencing the structural cenavior and safety were also investigated. Specifically, the structural analysis topics reviewed in more detail include:
~ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _
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(1) Dead loads and their effects.
(2) Buoyancy forces and their effects.
' (3) Variable springs used for the foundation modulus.
(4) Vertical earthquake effects.
(5) The side soil pressures.
(6) The boundary constraint conditions used for the mat.
(7) Finite element mesh size and its effects.
(8) BNL check calculations.
STRUCTURAL ANALYSIS TUPICS REVIEWED
- 1. Dead Loads (D)
As mentioned, EBASCO in their discussion and HEA in their reports have not shown analytically, the cause of the top surface cracks. In reviewing the HEA computer outputs, it was found that element moments and shears for indi loadings are explicitly given. Thus, for the case involving dead loads only, 'g ,Am I
a number of elements in the cracked regions exhibit moments (positive in sign) that can produce tension and thus create cracking on the top surface. Thi s situation is shown in Table 1 which gives moment data (Mx, My and Mxy) MM for elenents under various load conditions (dead (D), bouyancy (B) and normal N
side pressure) in some of the cracked regions. The particular elements are e Ip also depicted by the shaded areas shown in Fig.1.
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TABLE 1 l
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ELEMENT D B D B D B Mx .Mxy, 4 37 -242 173 -574 19 7 116 - 31 -294 -196 ,.
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.' 50' 7 441 -105 168 172 -170 39 - 12 -347 -489 66' l
Z E 436 -719 269 -1193 357 531 -130 -274 -258 ' 117 J2 7 4 38 269 142 -159 158 - 60 26 -730 -347 27 T -447 665 59 210 88 248 - 55 -653 -339 -127
? - 204 193 87 569 72 -143 28 -361 -420 24,
-208 350 32 898 - 24 -241 75 -354 -771 , - 49 203 -676 260 -995 236 39 - 21 -574 -247 30 426 -542 157 -705 310 332 - 65 -171 -486 61
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Fig.I LocATIQN oF E LEMENT6 LIST E D IN TAlbte.1. '
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Fran the HEA report (page C-2-1-9) it seems that the top reinforcement, which is #110 6" in each direction
- is the minimum requiremnt for tempera-ture steel according to the American Concrete Institute Building Code Speci-fication (i.e., As = .0018 x 12 x 144 = 3.11 2in /f t). The resisting moment capacity based on working stress design .is given by the expression M =
Assf jd, which can be approximated as 3.12 x 24 x 131/12 = 817 ft-kips /ft. p In view of the fact that tenperature and shrinkage cracks may exist in the base mat prior to the application of the dead load, the working stress design based on a cracked section used here is considered appropriate.
In checking the data shown in Table 1, it is to be noted for example, that for element 208, the dead load (D) mounts Mx and M y are respectively equal to 350 and 895 ft-kips /ft and are positive. Thus as mentioned pre-viously, the top surface is in tension. The maximum principle moment is a function of Mx, My, and Mxy and its computed value is close to 1000 g ki p-f t/f t. This moment exceeds the working stress capacity and thus cracking wil l_ occur. Similarly, concrete cracking could occur under the dead load condition in elements 447, 212, 204, 253, 255, 269, 257, 417, and 404. Thus, the cracks on the upper surface outside of the shield wall could have been initiated after construction of the superstructure, before placement of the back fil l .
- In a subsequent phone conversation, P.C. Liu of EBASCO stated that some addi-tional reinforcement was added on the top surface in one direction. This was l verified in the sketch depicted in Fig. 2 given to BNL by EBASCO where certain areas of the mat are shown strengthened with additional #11 bars are placed every 12 mdes in the east west direction.. Even if this is the case the .
1 statement that follows is true for the unstrengthened direction and probably even for the strengthened direction.
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In vieE of t3e' conments made in a later section in this report regarding i the finite element grid size and hence, their effects vis-a-vis, the accuracy e
i of the results, an approximate analysis of a strip of the mat was made. This
! strip was taken at the center of the reactor building in the N-S directioa f
with a width of 22 ft. In this analysis the mat was considered to be
- infinitely stiff and sub;ected to the dead loads taken from the HEA computer a
i np ut. The maximum moment for this case (i.e., 3450 f t-kips /ft) occurs close to the center of the reactor and indeed results in tension on the top surface.
This magnitude exceeds the cracking __ cap.c_i_ty of the mat which..i_s_in the neighborhood of 1764 f t-kips /_ft. Somewhat lower but similar results would occur at the other cracked sections shown shaded in Fig.1.
Thus, in summary, the cracking is most probably caused either by dead loads alone or by dead loads acting on elements somewhat weakened due to previous thermal and shrinkage effects. Essentially, for the latter case, the dead load moments would enhance previously existing small and most likely non observable cracks causing theti to become larger and hence, observable.
As shown in Table 1 and in Fig.1, the discussion thus far only pertains to cracks outside of the shield wall. As shown in Fig. 3 crack patterns were also noted in March of 1977, internal to the shield wall. At that time the shield wall was partially constructed up to elevation 187' and the steel con-tainnent was supported on temporary footings. Other walls or structures on the mat were either not as yet constructed or were only partially con-s truct ed . Since the computer dead load calculations refer to the mat with all_
4eti na <* *"""% it is not possible to utilize the computer results to explain the 1977 cracks. It should be pointed out however, that the additional top reinforcenents (i.e., # 11 W 12" shown in Fig. 2) are essentially located in areas under the shield wall and are placed in an east-west direction. Thus, if cracking should occur the preferred direction would
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be parallel' to the' direction of the heavier reinforcement. This is indeed the direction of the cracks. They could be due to curvature during construction and dead loads acting'in conjunction with thermal and shrinkage effects.
The additional east-west direction top reinforcements will also cause prevailing cracks in elements located directly east and west outside of the shield wall circle (i.e., those shown shaded in Fig.1 in areas R-P-2M-1A and R-P1-12A-9M) to be orineted in an east west direction. This is indeed the
- pattern indicated in Fig. 3. Since there is no additional top reinforcement in the elements shown shaded in Fig. I located between sections T2-R-12-7FH, the prevailing cracks do not necessarily have to be oriented in the east-west di rection.
- 2. Buoyancy Forces (B)
The moment results from this analysis show that these forces when acting alone would mostly cause tensile stress on tne upper surfaces. The moments causing these stresses are tabulated 'in Table 1 under the column heading B for groups of elements in the cracked regions. As can be seen, these momants are not as severe as those due to dead weight. By superpositon they could in some cases contribute to higher tensile stresses and thus result in further cracking in some of the upper surface areas.
- 3. Variable Springs used for the Foundation Modulus Moments and shears developed in the basemat were computed using the con-cept of the Winkler foundation; namely the soil is represented as a series of relatively uni form independent springs. The stif fness of the springs is ob-tained from approximate analyses which are based on generalized analytical solutions available for rigid mats on the surface of elastic soils. The actual design of the mat was based on a series of iterative computer runs in which the soil stif fness was varied until the computed contact pressures under the mat were f airly uniform and equal to the overburden stress at the eleva-
-8 This approach appears to be reasonable when as-
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sessing the final _ stress conditions. Long tenn consolidation effects can be
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anticipated to cause effective redistiribution of loads and cause the mat to behave in a flexible manner. However, during the initial loading stages this approach is not recmmended since load redistribution is continuously taking pl ace.
- 4. Vertical Earthquake Effects Vertical earthquake effect was not discussed in the HEA reports. However,
- from the finite element analysis print out and conversation with HEA engi-neers, it was stated that this effect was included in the load combination cases by specifying an additional factor of 0.067, which was then applied to the dead and equipment load case. From the discussions and the review it is not clear to BNL whether an amplification factor due to vertical mat frequency was used or not.
In order to obtain a rough estimate of tnis ef fect, the north-south direction of the mat was simulated by a beam on ' fourteen elastic sup port s.
The total weight of the mat, the superstructure, the equipment, etc. and the spring constants wre the same as those used by Ebasco and HEA in their camputer run. The natural frequencies obtained from this analysis are shown below in Table. 2.
Table 2 Natural Frequencies MODE CIFCULAS
""EQUENGY 'REQUENCY FEMOD-
- NUH6ER (SEC)
(RA0/SEC) (CYCLES /SEC) 1 .2863E*02 .4557E+01 . 219 6 E + 0 0
.3335 E+0 2 .530SE+01 .1884E+00 2
.3615E+02 .5753E+01 .1738E+00 3 .
. 37 21 E + 0 2 .5923E+01 .16tSE+00 4
.3902E+02 .6210E+01 .161GE+00 5
.LL20 E*0 2 .7035E+01 .1422E+00 6
.4007c+01 .12a 9 E
- 0 0 7 .5031E+02
.6645E+G2 .1058E+02 . 9 45 6E-01 a
.8135E+02 .1295E+02 .7724E-01 9
.1112E+03 .1769E+02 .5653C-01 to
.1262E+03 .2009E+02 .4919E-01 11
.154eE+03 .2661E*02 6066E-01
, 12 176t E + 0 2 . 317 9E- 01 13 ,.2"b1E+03 1% .2357E*03 .3/$2E+02 .2tt6E.01
[ .
. 9- .
As can be seen from the table, the frequencies vary from 4.56 to 37.52,
~
,. cp s. Using Regulatory Guide 1.60, for the 5% damping case, it is found that amplification factors for these frequencies will vary from 3.0 to 1.0, For l
the first seven frequencies shown in Table 2,- the amplification factors will be less than 3.0 but above 2.60. From the review it seens that the vertical amplification factor used by HEA was 1.34, which is below 2.60. It should be realized, however, that not all response parameters (moments, shears, etc.) are sensitive to these frequencies. Moreover, the frequencies were obtained from a simplified model. Hence, to apply an overall amplification factor of say ,
for instance even 2.5 to all response parameters is not reasonable. This P
situation usually will result in some local effects, such as, increasing the seismic moments at some particular locations. Where this increase occurs is l
hard to ascertain without perfoming a very detailed dynamic analysis. Since the effects are localized, it is felt that they should not greatly influence the total resultant stresses acting on the mat.
It should also be realized that the reviewers used Reg. Guide 1.60 to l
! obtain the rough estinates for amplification factors. The guide spectrum is a wide band spectrum that reflects amplifications based on statistical samples of earthquake records. Thus, it is possible that site specific earthquake records could yield lower amplification factors.
- 5. Side Soil pressure According to the STARDYNE computer results obtained from HEA, the nomal side soil pressures produce large moments that are opposite to those caused by the dead loads. As shown in Table 1 where moments of elements located in one of the cracked regions outside of the shield building are compared. The total moments in some cases (i.e. element 447 or 208) becane quite small. In other regions there is in fact a reversal in the total bending moment which causes tension on the bottom surface and conpression on the top. This conpression would tend to close the cracks on the upper surface. Thus, it appears that this pressure is a very important load case for the mat design.
i
For the . static or. normal operating condition tne lateral pressures are
~'
based on'the at-rest strest condition and are uniform around the periphery of the structure. For the seismic problems the pressures are computed to approximately account for relative movements betwen the structure and the soil. On one side the structure will move away from soil (active side) and reduce the pressures while the opposite will occur on the other side (passive side). The actual computations made use of site soils properties to arrive at the soil pressures rather than the standard Rankine analyses. No dynamic effects on either the lateral soil or pore pressures was included. The ,
sensitivity of the calculated responses to these effects are currently unknown. However, approximate estimates of these dynamic effects indicate that total lateral load should change by no more than 15 per cent.
- 6. Boundary Constraints For equilibrium calculations no special consideration need be made for yi
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1 vertical case since the soil springs prevent unbounded structural motion.
- However, the same cannot be said for the horizontal case since soil springs are not used to represent the soil reactions. Rather the lateral soil forces are directly input to the nodel. To prevent unbounded rigid body motion, ar-tificial lateral constraints must be imposed on the model. The constraints are depicted in Fig. 4. The nodes shown circled were constrained from move-ment in the y direction, while those described by "x" were constrained in the x direction. As cmmonly practical in finite element applications, the con-straints are placed in a manner that they do not overly affect the static and dynamic response cal culations. From the output presented in the EBASCO and HEA reports, it is not possible to evaluate the impact of the above shown boundary assumptions. The stresses caused by the artificial boundaries should be calculated and compared with those presented.
- 7. Finite Element Mesh and its Effects In general finite element models for plate structures require at least four diements betwen supports to obtain reasonable results on stress comp-utations. The models used by both EBASCO and HEA violate this " rule of thumb"
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in the vicinity of the'shie.ld wall. The significance of this effect is demonstrated 'iri Figure D-3 of Report No. 8304-2 which presents a plot of moment taken through the center of the slab. The computed moments in adjacent el ements 193,194 and 455 are -3800, -2500 and +400K. The elements used in the HEA analysis are constant curvature elements so that the canputed moments will be constant within each el'ement. The steep moment gradient between the elanents indicates that a finer mesh would be advisable. A similar effect was t
also noted when investigating the elements forming the junction between the lateral earth retaining walls and the base mat. 3
- 8. BNL Check Calculations Due to the questions raised in the items above (4 through 7), it was de-4 cided to perform several calculations to verify the acceptability of the mat design.
l
- 1. Average Vertical Shear Several elenents in the Ebasco/HEA analysis indicate local areas where al-lowable shear stresses are exceeded. Shear failure should not be associated with local exceedance of an allowable shear stress. Rather, one should_ con _
sider the average shear _ stress across an entire failure plane in the mat. All j
of the ACI code shear requirements are based on this approach. Two types of average vertical shear stresses (i.e., diagonal tension) were computed in the base mat. The first type considers the average shear through a vertical sec- ,
tion across the entire mat (one section in the E-W direction and the other in the N-S di rection). These sections were chosen to include those elements which indicated high shear stresses in the HEA analysis and where the actual cracking pattern was noted. The highest average shear stress computed for any design load combination is 50 psi. The allowable shear stress for the case is 107 psi (4/fc). Thus, a safety factor greater than two is available to prevent catastrophic shear failure under the design load combination.
i 1
0 I
= __
- 2. Punching Shear The second type of section considered is a circular punching shear section located a distance of d/2 outside the reactor shield wall. The peak value of shear stress due to both SSE overturning moments and normal operating loads (plus proper load factors) were close to but always less than the allowable design shear $4 /fe).
- 3. Stresses Resulting From Pouring of Adjacent Mat Blocks 3 Comments have been made that diagonal tension cracks occurred during the process puring adjacent mat blocks. To estimate if such cracking is possible an approximate analysis was made. It is included in Appendix B. The adjacent block are assumed to rest on foundation springs which represent the soil flex-i bili ty. The second block to be poured was assumed to harden instantaneously thereby overestimating the shear load carried by the first block due to relative settlement of the two blocks. The resulting stresses were found to be sufficiently small so that neither diagonal tension nor bending tensile
! stresses would be expected to cause cracking. The likelihood of moment cracking was greater than for shear cracking. These conclusions are valid even for the case with sof t spots in the foundation where ene soil modulus is one half the other.
e It shou'd be noted that the soil settlenent at the site is found to be instantaneous based on actual measured data. The concrete has almost no strength for the first twelve hours and therefore even the small stresses calculated in Appendix 8 are unlikely.
(4) Side Loads Under normal operating conditions the loads acting on the side walls pro-
- duce an average compressive stress in th'e base mat of aoout 50 psi. When seismic loads are included, the average canpressive stress in the base mat is l about 38 psi. These compressive stresses provide additional shear strength I
i
which have not been included in evaluating the capacity 'of the mat to carry
~
di. agonal tens' ion stresses. It should be noted that the average maximum dia-gonal tension requirenent in the base mat is only 50 psi. Therefore, the potential for the separation of the mat into two halves is unlikely even if a :
true through crack existed across the entire mat. This analysis is presented in Appendix C. -
CONCLUSIONS AND RECOMMENDATIONS s
(a) The Waterford plant is primarily a box-like concrete structure sup-ported on a 12 foot thick continuous concrete mat which houses all Class 1 structures. The plant island is supported by relatively soft overconsolidated soils. To minimize long term settlement effects, the foundation net was designed on the Coating. foundation principle.
The average contact pressure developed by the weight of the structure is made approxinutely equal to the existing intergranular stresses developed by the weight of the sofi overburden at the level of the '
bottom of the foundation mat. Thus, net changes in soil stresses due i to construction and corresponding settlements can be anticipated to be relatively small. ,
(b) In reviewing the infornation, reports, and conputer outputs sup-i plied to BNL by EBASCO, HEA, and LPL, it is concluded that nor-mal engineering practice and procedures used for the analysis of nuclear power plant structures were employed.
(c) Accepting the information pertaining to loadings, geometries of the structures, noterial properties and finite elenent mesh
! , data, it is the judgement of the reviewers that:
i (1) the bottom reinforcenent as well as the shear capacity of the base mat are adequate for the loads considered.
(ii) the c m puted dead weight output data can be used to explain
~
^ some of the mat cracks that appear on the top surface. The cracks that appear, could have occurred after the construction of the superstructure but before the placement of the backfill.
Their growth would then be constrained by subsequent backfill soil pressure.
(d) Due to the existance of the cracks, it is recommended that a sur-veilance program be instituted to monitor cracks on a regular basis. ,
Furthermore, an alert limit (in terms of amount of cracks, and or crack width, etc) should be specified. If this limit is exceeded, specific structural repairs should be mandated.
(e) It is also recermnded that a program be set up to nonitor the water leakage and its chmical content.
(f) BNL has reviewed the information provided by EBASCO, HEA, and LPL. The following questions concerning their analyses wre developed:
(1) d)tiamic coupling in the vertical direction between the reactor building and the base mat.
(ii) dynamic ef fects of lateral soil /witer loadings.
(iii) artificial boundary constraints in finite elments models.
(iv) fineness of base mat mesh.
Based upon our approximate calculations together with engineering judge-ment, we do not anticipate that the above questions will lead to major changes in calculated stress levels. Thus, it is our opinion that the safety margins in the design of the base nut are adequate. However, it is recanmended that sone detailed confirmatory calculations be performed in the near future to strengthen the above conclusions.
A-1 APPENDIX A-1 LIST OF CONTRIBUTORS Listed below in alphabetical order are the names of the contributors to this report:
Costantino, C.J.
Miller, C.A.
Philippacopoulos, A.J.
Reich, M.
Shanna, S.
Wa ng , P .C .
0
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Appendix B Stresses Inouced While Pouring Blocks s
e I
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c A question has been raised concerning the stresses which could have been introduced when the basemat blocks were being poured. The response of two adjacent blocks during construction are considered. The first block is taken to be in place when the secon'd block is placed. It is also assumed that the concrete in the second block hardens immediately so that it can transmit loads to the first block. The subgrade modulus under the two blocks is assumed to be different so that the ef fect of sof t spots in the soil can be considered.
A sketch of the problem to be considered is shown in Fig.1.
When the first block is poured it settles an amount, b =l W/K 1 The second block is then poured. If the concrete is conservatively assumed to harden before the soil settlement can occur, the second block will introduce l additional loadings on the first block. The new deformation caused by the weight of the second block is shown on Fig. 2.
The loads acting on the bloc'k may tnen be determined by multiplying the defonnations by the foundation moduli. Tnese loads are shown on Fig. 3.
Force and moment equilibrium allow the two unAnown displacements (d ,f/) to be calculated. The results are, b *2 W [(7 +b)/(1 + 14C+Q2)]/K 1
/ = 12 W/[L Ki(1+14h,+C2)][
where,h=K/K1 2
Once the displacanents are known the lohds on the blocks may ce evaluated and beam shears and bending moments may be computed. This is cone for foundation moduli ratios of 1. U.S. and U. Peak values of snear and moment are tabulated in Table 1.
I
Table 1
. Shear, and Moments in Blocks During Construction Foundation Maximum Required f'c (psi)
Moduli Ratio Shear Moment To Prevent
(()) (Kips) (Kip-ft) = Shear Bending Tension Failure Crack 1 563 5040 15 15 0.5 819 13770 31 113 0 4689 156375 1091 14559 For the design concrete strength of 4000 psi, the shear capacity of the concrete section is 9290 kips. As may be seen this is much larger than the peak shears that could be caused during construction. Bending cracks will occur in the concrete when the peak ' concrete tensile stress reasches the modulus of rupturo. For the concrete design strength this will occur at a bending moment of 81966 kip-feet. It may be seen that the peak moments are closer to the value required to cause a bending crack than the peak shears are to that required to cause a diagonal tension crack.
The concrete will not have attained its final strength at the time when these stresses occur. The last two columns in Table 1 list the required concrete compressive strength to prevent shear and moment failures. Two conclusions may be drawn from these data. First, even for rather dramatic variations in founaation moduli, only a minimal concrete strength is required to prevent either a shear or moment crack. Second, if a crack were to develop it would most likely be a bending crack.
The above analysis is based on the assumption that the concretc hardens before soil settlenent occurs. If this were not so, the wet concrete would
fill tne void volume created by soil settlement. The concrete block would then be supported on the soil rather than " hanging" from the other block.
Figure 4 shows the concrete. strength gain during'the first day. As may be seen concrete will have no strengtn until about'12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br />. By this time all of the soil settlement would have occurred and the second concrete block would not induce any loads on the first block.
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1 ' '*, . ening cement.s. (Adapted from W. Perenchio. In Ness Afarerfals in Concrete
- [gL' * . Construction. ed. S. P. Shah, University of I!!;nois at Chicago Circle. '
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- T . Chicago,1972. p.12 -VI.)
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M i w In the production of VHE cement, calcium sulfate is added to the raw ig mix so that CeA3 S is formed in the rotary kiln. This is the same compound that is present in Type K expansive cements, but the quan- '
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e Appendix C 4
Effect of Sidewall Loads On Basemat Capacity I
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' l I
1 I
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O
-Soil pressure loods act on the sidewalls and these loads introduce compressive stresses in the slab of the basemat. This compressive stress will assist in resisting the diagonal tension stresses which occur in the slab.
The significance of this effect is aiscussed in tne Appendix.
Table B.1 lists the horizontal loads which act on the sidewalls due to the various load combinations. These loads were detenmined directly from the
'HEA/Ebasco computer printouts. An elevation of the structure parallel to the long direction of the basemat is shown on Fig. B.I. The forces (P) are taken as the forces shown on Table B.1 and acting on walls #2 and #4. The soil
-pressure is assumed to have a triangular variation as shown so that the ,
resultant force (P) acts at the third point on the wall. Since the ' wall is buried _ about 54', the resultant force acts at a point 18' up the wall from the bottom of the basemat.
The stresses caused by this loading in tne cross section shown on Fig.
B.2. The basemat is analyzed as a beam structure. The cross section shown in Fi9. B.2 has the following properties:
Cross sectional area = 3552 square feet Centroid at 7.91' above tne bottom of tne mat 4
a = 247300 feet 4- d Moment of Stresses are the .,puted as:
f = P/A + t. : f I Tnerefore at the top of the wall, fwt = P/3 oz - F (18-7.91) (b4-7.91) ' 247300 The stress at tne t;p of tne slab is, f ts = P/3dez - P (18-7.91) (12-7.91) / t 73ua Tne stress at tne :s:ta:. of the slac is, fes = P/3t:2 - P (1o-7.91) (7.91) / 247:su
> The resultant stresses for'the Case 4 loads (Nonnal soil pressure) are:
f tw = 541 psi ,
f ts = 112 psi f bs * -11 Psi The stresses for Case #8 (SSE in N-S) are:
.ftw = 465 psi fts = 84 psi fbs = -8 psi The average stresses in the slab for these two load cases are 51 psi and 38 psi respectively. The average shear in the basemat for Case 8 loadings was.
found to be 50 psi. If this shear stress is combined with the 38 psi average '
compressive stress one finds tht the tensile stress in the concrete is reduced to 34 psi. .It is unlikely that this stress could cause a shear (diagonal tension) failure.
9
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Loaa. Case Wal1 #1 #2 #3 #4
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- . Case 4: Normal Soil Pressure 36619 36441 50942 50522 Case B: SSE & Soil (North to South) 27061 110657 50684 50377 26907 50684 50377 Case 10: SSE & Soil (South to North) 111051 m
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