ML20011A463
| ML20011A463 | |
| Person / Time | |
|---|---|
| Site: | Point Beach  |
| Issue date: | 09/30/1981 |
| From: | COMPUTECH ENGINEERING SERVICES, INC. |
| To: | |
| Shared Package | |
| ML19312F019 | List: |
| References | |
| IEB-80-11, R553.08, TAC-42896, TAC-42897, NUDOCS 8110130442 | |
| Download: ML20011A463 (49) | |
Text
. 1 i i
EVALUATION OF ALLOWABLE IN-PLANE SHEAR STRESSES AND STRAINS Prepared for Point Beach Nuclear Power Plant, Units 1 and 2 WISCONSIN ELECTRIC POWER COMPANY Milwaukee, Wisconsin Prepared by l
l COMPUTECH ENGINEER.NG SERVICES, INC.
Berkeley, California September,1981 REPORT NO. R553.08 0
kko$0 O
R
TABLE OF CONTENTS 1 INTRODUCTION . ... . 1 OVERVIEW OF TEST PROGRAM .. . . 2 2.1 Applicab lity of Test Results 2 3 EVALUATION OF TEST DATA . . 4 31 Shear Stresses and Strains for OBE and SSE Events . . 4 32 Statistical Analysis of tne Data . . 5 3.2.1 Shear Strain Results 6 3.2.2 Snear Stress Results . 8 3.3 Discussion of Results .. . . . . 8 4 SPECIFIC RESPONSE TO ACTION ITEM 6 .
. 10 5 CONCLUSIONS .. . . 13 6 REFERENCES .... . . . 14
1 INTRODUCTION The Nuclear Regulatory Commission staff on June 9-11, 1981. reviewed the criteria and calculations performed on IE Bulletin 80-11 " Masonry Walt Design' for the Point Berch Nuclear Power Plant. Action item 6 resulting from that meeting stated that with regard to in-plane shear evaluation the licensee shall provide the following.
A. Statistical summary of test data presented at the meeting to develop the strain values Corresponding to mean, le. 2&! and 30' levels with 95 % confidence intervals for both OBE and SSE consideration.
Also. determine the probability of exceedance corresponding to the four strain level values used in the criteria.
- 8. Nominal allowable shear stress corresponding to OBE and SSE strain values accounting for degradation (30 %) based on the above test results. In no case shalt this value exceed 43 psi.
C. Discussion and technical oasis that test data utilized in developing item 6.a are pertinent for Point Beach masonry wall reevaluation application. e.g., aspect ratio. f' . mortar strength.
D. Technical discussion of the state of deformation of masonry walls (e.g.,
initial cracking and significant cracking as defined by limiting strain values, crack pattern and propagation). Also, discuss the safety significance of the walls at these strain levels, e.g., safety margin with respect to the loss of wall function.
E. Evaluate the effect and assess the impact on out-of-plane stiffness due to in-plane cracking at these four strain levels.
This report provides the information on the five items above, except that data on the strain leve!s for unconfined walls is not provided because the tests performed in the Berkeley research program only apply to confined walls.
The report is subdivided as follows: Section 2 provides an overview and discusses tne applicability of the test program from which the test data is obtained.
Section 3 presents an evaluation of the test data. and Section 4 provides the specific response to each of the five items. Section 5 presents the conclusions.
t
2 OVERVIEW OF TEST PROGRAM The results from an ongoing masonry test program being performed Et the Earthquake Engineering Research Center. University of California, Berkeley, are used in this report to evaluate the in-plane shear strength and strain of masonry piers. The results of the research have been reported in References ' 2, and 3 and basically consist of subjecting masonry plers to an in-plane cyclic shear load with the test set-up shown in Fig.1. The piers are tested by applying three cycles of load at a specified amplitude. The amplitude is gradually increased as the test progresses until the pier is unable to resist any further load. Each test was photographed after each set of three cycles of load, thereby providing detailed records of the crack patt3rn.
To date over ninety piers tsave been tested using three different types of materials.
Thirty-five of the piers tested were constructed from hollow concrete block masonry units and of these six had a height-to-width ratio of 1 to 2. fifteen had a height-to-width ratio of 1 to 1. and fourteen had a height-to-width ratlo of 2 to 1. The piers were constructed frc.m either 6-inch or 8-inch wide hollow concrete block units using Type M mortar. The strength of prisms constructed from the same materials that were used l'a che piers varied from 1350 to 3000 psi.
The informatan obtained from each test consisted of a plot of the force-deflection relationship for each cycle of loading. From this set of curves several parameters could be determined. including:
(a) Ultimate strength (b) Stiffness degradation (c) Hysteresis envelope (d) Deflection of pier at each loading stage 2.1 Applicability of Test Results The information obtained from the BerMley test program is valuable in evaluating the in-plane shear performarce of masonry piers subjected to selsmic loads. A discussion on the applicability of the test results is discussed separately with respect to the following variables -- loading, size of test specimen, boundary conditions, material strengths and reinforcement.
A. Loadino Although an earthquake type time history was not used as the input motion to the test specimen, the gradually increasing, amplitude dependent, cyclic loading was typical of that used in many other test programs on reinforcad concrete and steel structural elements. The most import ni aspect .' hading required to evaluate the seismic performance of structural elements is that tiie loading be cyclin or reversed. Other variables such 2
_ __. _ _ _ _ ~ - __ _ _ _ __ . _ _ _
as the rate of loading, sequence 01,m S. etc. may be important but are secondary in comparison to the reqv;eement that the tuawng be cyclic.
B. Size of Test Soecimen The size of the test specimen used in the Berkeley test program was limited by the capacity of the actuators. The piers with a height-to-width ratio of 1 to 2 were 3 ft. 4 inches high and 6 f t. 8 inches long, the 1 to 1 piers were 4 ft. 8 inches high and 4 ft. long whereas the 2 to 1 piers were 5 ft. 4 inches high by 2 ft. 8 inches long. Although these sizes are generally smaller than the walls found in the Point Beach Nuclear Power Plant.11 is assumed that they are of adequate size to represent the behavior of larger sized walls with the same aspect or height-to-width ratio. It should be noted that no experimental evidence is available to validate or refute this assumption.
The aspect or height-to-width <atios included in the test program er ar all the walls at the Point Beach Nuclear Powdr Plant.
C. 22undary Conditions The boundary conditions of the plers tested in the Berkeley program were such that moment fixity was forced at both the top and bottom of the piers with no constraina on the vertical edges.
Although this set of boundary conditic's is different to that of most of the walls at the Point Beach Nuclear Power Plant, it is believed that if the walls at the plant are confined either on three or four sides or at the top and bottom, then the performance of the walls will be similar to those tested in the Berkeley program. Confinement should be provided by either walls or columns capable of resisting the loads imposed by the concrete block walls. Unfortunately there is no test data available for the boundary conditions typically found at Point Beach Nuclear Power Plant.
D. Material Strenoths The average compressive strength f' of prisms taken from the walls at the Point Beach Nuclear Power Plant was 1942 psi. This is within the range of 1350-3000 psi of the prism strength of the piers included in the Berkeley test program.
E. Re8nforcement The majority of the walls at Point Beach Nuclear Power Plant are unrelnforced whereas all the piers of the Berkeley test program were reinforced, it is our tatief that provided the walls at the Point Beach Nucleer Power Plant are confined on three or four sides 'or at the top and cottom. then cracks in the unreinforced wall will occur at similar strain levels to the piers tested.
3
3 EVALUATION OF TEST DATA The data from the thirty-five tests performed on hollow concrete block piers was evaluated on the basis of both shear stress and strain. The shear strain criteria was primarily used to evaluato thn in-plane adequacy of the masonry walls at the Point Beach Nuclear Power Plant becaese they were infill walls and were not part of the structural resisting system. lherefore, in-plane loads on the wall result from imposed deflections. This merns that the loads are self-limiting and are related to the interstory structural displacements. The most reasonable approach to evaluate the adequacy of the walls subjected to imposed displacements is to determine the deflection or strain the wall can resist.
Consequently more emphasis is placed on this variable in the following sections.
Unfortunately the Berkeley test data is only applicable to confined walls. The criteria developed for unconfined walls (i.e.. supported on only one vertical side) was conservatively based on judgment. It was felt that 14tial cracking in an unconfined wall would occur at larger strain values than a confined wall.
However, once cracks develop, the lack of confinement may cause instabilities that could not be tolerated. Thus the allowable strain for unconfined walls was specified as one-eighth of the confined value.
Section 3.1 explains how the tost data was evaluated to determine the permissible strains for both an OBE and SSE event. Section 3.2 provides a statistical evaluation of the data and Section 3.3 presents a discussion of the results.
3.1 Shear Stresses and Strains for OBE and SSE Events The test results from the Berkeley program were evaluated to determine in-plane shear stresses and strains appropriate for an OBE and SSE event.
The evaluation was performed so that the function of a wall would not be impaired while it was resisting out-of-plane loads. During each pier test. photographs were taken after each set of three cycles of load at a specified amplitude. These photographs in conjunction with the hysteresis envelopes developed for each test were used to determine the appropriate state of cracking due to in-plane loads that could be tolerated from an OBE and SSE event. For an OBE event the loading stage at which initial visible cracks occurred was used. For an SSE event additional cracking
- was permitted, however the loadg stage was prior to any significant diagonal cracking. Obviously the evalu tion for an SSE event required judgment and photographs shown in Figs. 2. 3. and 4 show the typical state of cracking used for both an OBE and SSE event for piers with height-to-width ratios of 1 to 2. I to 1. and 2 to 1 respectively. At each appropriate level of cracking the corresponding shear stress and displacement were determined.
The displacement was divided by the wall height to determine a corresponding shear strain. The shear stresses and shear strains obtained were statistically evaivated and these results are presented in the following subsection.
l 4
~ - - . . -
l 3.2 Statistical Analysis of the Data A total of 34 and 35 tests were used to evaluate the shear stress and strain for tne OBE and SSE events respectively. The shear stresses and strains were determined oy the procedure c.escribed in tne foregoing subsection.
From this data tne following parameters were calculated for the shear stress and snear strain for both the OBE and SSE events.
(i) Sample mean. X (ii) Sample standard deviation. s These statistics were tnen used as tne parameters for the distribution of tne popuiation. For each case COBE and SSE). two underlying distributions were assumed. and the effect of tne cr'oice of distribution on the results was examined. Tne more reasonaote distribution was then accepteo. The two underlying districutions were tne normal distribution and the gamma distribution, and tne gamma distrioution was cnosen as best representing tne test data for reasons given in Section 3.2.1.
The 95 % con idence interval for tne mean of tne population M s
was calculdied. assuming that the norma!Ized variable X-M s/ qY is t-distributed, and that the actual population standard deviation, 0. is unknown. Here n is the sample size.
- For the gamma distribution, confidence intervals on parameters such as M, - M ;-k o . have no meaning, and must be reinterpreted. On the normal curve lo' corresponds to a point on the cumulative distribution curve with an ordinate of 0.1587. Tnis means tnat approximately 16 %
of the area under Ine probability density curve lies to the left of M Similarly M - 20 and M- 30' correspond to points with ordinates 0.02275 and 0.00135 respectively. Based on tne confidence interval for the mean.
Confidence intervals were calculated for values of the gamma distribution for which the cumulative distribution function had values of 0.1587. 0.0025 and 0.00135 respectively.
These actual distr:Dutions were then compared with the criteria specified al;owabie shear strains and stresses, i.e.
0.0008 and 0.9 ff' . respectively for the OBE condition, and 1.67 and 1.5 times, these values, respectively for the SSE condition. Probabilities that the criteria specified allowable strain would exceed the actual strain based on tne test results were calculated under two assumptions: firstly, tnat tne population mean was equal to the sample mean and secondly, tnat it was at the tower end of the 95 %
confidence inter al Finally, safety factors based on tne 95 % confidence interval for the mean es, S
r were calculated for both the shear strain and shear stress.
3.2.1 Snear Strain Results OBE SSE Sample Size 34 35 l Sample Mean 0.00202 0.00318 Sample Standard Deviation 0.00085 0.00094 Coefficient of Variation 42 % 30 %
The 95 % confidence intervals on the population mean are:
OBE 0.00172 5 M ( 0.00232 SSE 0.00286 4 M 4 0.00350 The effect of the assumption of normal distribution versus the assumption of gamma distribution was studied. A plot of the histograms of test data for both the OBE and SSE conditions are shown in Fig. 5. Two observations are as follows.
(i) The data never takes on negative values.
(ii) The distribution of data is skeweo, especially for the OBE condition.
Both of these observations indicate that the gamma distribution !S preferable to tne normal distribution. The gamma distributfor is dafined t.v f (x)= h, (kx) e xyG (k-1)l and has a mean value of k/A and a coefficient of variation of 1/8 The following values of k and x give best fits to the OBE and SSE data:
Case k K.
OBE 6 2970.3 SSE 11 3459.1 These curves are also plotted in Fig. 5.
It should be noted that there is no physical reason why shear strains should have any particular distribution. However, by suitable adjustmer.t of the parameters k and A , th9 gamma distribution can be made to describe the best data far more accurately than can the normal 6
-s +-
m-* + g p o-t p ----m, p,pw,,-g m --~ - - - - y -r >-m m -, -----1.y-ye- mm v +yv
l l
distribution.
The 95 % confidence intervals corresonding to the lo. 20'. and 30' levels are as follows:
(i) Corresponding to cumulative distribution function = 0.1587 (10' level)
OBE 0.00090 ( X 4 0.0014S SSE 0.00192 ( X ( 0.00257 (ii) Corresponding to cumulative distribution function = 0.02275 (20 level)
OBE 0.00045 ( X 4 0.00091 SSE 0.00129 4 X 4 0.00189 (iii) Ccrresponding to cumulative distribution function = 0.00135 (3cr level)
OBE 0.00020 ( X 4 0.00053 SSE 0.00081 4 X ( 0.00134 Using the allowable strain values from the criteria for confined walls and the above 95 % conflderir,e interval on the mean the following ilmits on the factor of safety are established:
OBE: 2.15 ( SF f 2.90 SSE: 2.13 ( SF ( 2.61 Thu probaYlities that the criteria specified strain values will exceed the available strain capacity based on test results and the gamma distribution are then as follows:
Key OBE SSE A G.034 0.008 8 0.119 0.029 Notes: The key A gives the probabilities of er .edance assuming the population mean equals the Mmple mean. B gives the probabilities of exceedance usuming the population mean is (.t the lower end of the J5 % confidence interval.
7
. _ . ~ . , -. ._.
3.2.2 Shear Sussa Results OBE SSE Sample Size 34 35 Sample Mean 154.7 psi 178.7 psi Sample Standard Deviation 62.1 psi 76.1 psi The 95 % confidence intervals on the mean are as follows:
06C: 133.1 psi ( M ( 176.3 psi SSE: 152 6 psi ( M f 204.8 psi Using the allowable stress values from the criteria with f' = 1.000 psi and the above 95 % confidence intervals on the mean. Ee following limits on the factor of safety are established:
OBE: 4.68 4 SF 4 6.19 SSE: 3.57 ( SF 4 4.80 3.3 Discussion of Results The main value of the test data generated in the Berkeley test program is that it enables a reasonable estimate of the deflections or strains at which various levels of cracking could be expected in a masonry wall.
Because of the differences in the test specimens and the walls at the plant, it is our belief that the shear stress data is not as useful in evaluating the in-plane adequacy of the walls. Furthermore, since the deflections that an infill wall will be subjected to are self-limiting. It is our opinion that a lower factor of safety is acceptable when compared to, say. an allowable shear stress for a load-bearing snear wall.
By taking the 95 % confidence intervals on the population mean, the factor of safety associated with the allowable strain at 0.0008 for an OBE event is 2.15 ( SF ( 2.90. For an SSE event the corresponding range is 2.13
( SF ( 2.61 based on an allowable strain of 0.0017. In terms of probability, it can be stated that code allowable strain will exceed the actual strain obtained from the testa 34 times in 1000 for OBE events and 8 times in 1000 for SSE events if the population mean strength is taken at the center of the 95 % confidence intervals. If one considers the extreme case where the population mean is taken to be at the lower end of its 95 % confidence interval then these figures become 119 times in 1000 for OBE events and 29 times in 1000 for SSE events. Given the extreme nature of the assumption on which these second estimates are based and the self-limiting natue rf the load, these probabilities of exceedance are deemed satisfactory.
Although we recommend less reliance on the shear stress values obtained from the test data, the range of the factor of safety based on the 95 %
confider.ce interval for the population mean is reasonably high. For an 8
V OBE event the range is 4.68 i SF ( 6.19 and for an SSE event it is 3.57
( SF ( 4.80. Therefore the values specified in the criteria are reasonable.
t i
1 i
l l
9 i
4 SPECIFIC RESPONSE TO ACTION ITEM 6 The preceding sections provide background information and a summary of the test data required to respond to eacn of the five parts of Action l'.em 6. The response to each item follows.
A. Statistical summary of test data presented at the meeting to develop the strain values corresponding to mean. le 2c' and 30 levels with 95 % confidence intervals for both OGE and SSE consideration.
Also, determine the probability of e ceedance corresponding to the four strain 'evel values used in the criteria.
The statistical analysis of the strain values is given in detal in Section 3.2.1. and a discussion of the resuits is given in Section 3.3. It should be noted that data pertaining to the two strain levels for unconfined walls is not presented because the test results were not applicable to unconfined boundary conditions. Tne range of the factnr of safety for confined walls based on the 95 % confidence interval on the population mean is 2.15 ( SF ( 2.90 for an OBE event r nd 2.13 ( SF ( 2.61 for an SSE event. These factors of safety are considered reasonable when the loading of an infill wall is by imposed displacements and is therefore self-limiting.
The values specified in the criteria for unconfined walls are one-eighth of the values specified for cor. fined walls and this conservative estimate based on judgment is considered to be reasonable.
B. Nominal allowable shear stress corresponding to OBE and SSE .: train values accounting for stiffness degradation (30 %) based on above test results. In no case shall this value exceed 43 pst.
The shear stresses, correspc .J ng to the strain values at which the test data was evaluated, were analyzed to determine a range of the factor of safety for the criteria specified allowable stresses based on f' = 1000 psi. The range was cased on the 95 % confidence m
in'.erval of the population mean of tt.e test data and was 4.68 (
F.F ( 6.19 for an OBE event and 3.57 ( SF ( 4.00 for an SSE event.
Although we rocommend that less reliance be placed on the shear stress values, the values used in the criteria are reasoncble.
C. Discussion and technical basis that test data utilized in de'veloping item 6.a are pertinent for Point Beach masonry wall reevaluation application e.g., aspect ratio f' . mortar strength.
This discussion is prosented in detail in Section 2.1 and covers the type of loading. the size and aspect ratio of the test specimen.
boundary conditions. material strengths and reinforcement.
D. Technical discuWn of the state of deformation of masonry walls (e.g..
in.nal cracking .tr. ) significant cracking as definer' by limiting strain vasues, crack pattern and propagation). Also. F, cuss the safety 10
significance of the walls at these strain levels, e.g.. saferf margin with respect to the loss of wall function.
The typical state of cracking chosen for the OBE and SSE events is shown in Figs. 2, 3. and 4 for piers with height-to-width ratios of 1 to 2, 1 to 1, and 2 to 1 respectively.
For the OBE event the state of cracking corresponds to the first visible cracks in the piers. These typically occur across the head jofnts and have no impact on impairing the safety of the walls. The cyclic behavior of the plars at these displacement levels is essentially non-linear elastic with some associated stiffness degradation.
For the SSE event a greater amount of cracking was permitted although the stage of Ic3 ding chosen was always prior to the formation of any significant olagonal cracks and inis always corresponded to a stress level prior to the ultimate stress attained in each test. As such, there would be no strength reduction associated wit's this level of loading although there would be stiffness degradation of the order of 30-50 %. The hysteresis curves at the SSE load level shows that the cyclic behavior is essentially non-linear elasti' with a small amount of energy cessipation resulting from the c/clic behavior.
There would be no loss of wall function because of the conservatism used in selecting the appropriate load level for the SSE event.
Furthermore, as the load imposed on an infill masonry wall is displacement limited by the overall structure, the limits established by the OBE and SSE events are considered to be reasonable.
E. Evaluate the effect and assess the Impact on out-of-plane stiffness due to in-plane cracking at these four strain levels.
The Point Beach FSAR provides for the design of a two-direction (one horizontal and one vertican earthquake. The implication of this requirement is that the in-plane and out-of-plane perforraance of the walls can be considered separately. However. since I,oth new and SEP plants are required to consider three components of earthquake, the evaluation of the in-plane shear strain was perfi rmed so that the out-of-plane performance of the walls would not be impaired.
Unfortunately, there are no test results available te, evaluate the combined effect of in-plane and out-of-plane loads, thus judgment must be used in evaluating the in plane shear test results.
For the OBE event the minor initial visible cracks used to determine the appropriate load level, in our opinion, would have no impact on the out-of-plane performance of the walls.
For the SSE event. more cracking was permitted, however. most of this occurred away from the center of the wall and was diagonal in nature. It is our belief that the nature and amount of cracking permitted for the SSE event would have little impact on the out-nf-plane performance of the walls, it would be expocted that there would be smie stiffness degradation associated with the 11
6 out-of-plane stiffness. The actual amount of degradation is difficult l
to assess. Dut we believe it would not be excess ve. r O
b 12
4 5 COfvCLUSIONS The purpose of Action item 6 was to provide a detailed analysis of the Berkeley test data to justify the allowable shear stresses and strains used in tne reevaluation criteria. The allowaole strain was primarily used to evaluate the in-plane adequacy of the walls at the Point Beach Nuclear Power Plant decause they were infill walls and were not part of structural resisting system. The in-plane loads on the wall result from imposes interstory structural displacements wnicn are self-limiting in nature. Therefore, greater emphasis has been placed on the allowable strain in the statistical evaluation of the data. Because the test setup used in the Berkeley program did not include a simulation of an unconfined wall, the values given in the criterla for this condition were not evaluated.
Tne range of the factor of safety for confined walls for the allowable strains given in the criteria were 2.15 ( SF { J.90 for an OBE event and 2.13 ( SF
( 2.61 for an SSE event. These factors of safety are based on the 95 %
confidence intervals of the mean strength of the population. Given the self-limiting nature of the deflections or strains to which the walls would be subjected, these values are considered reasonable for the Point Beach Nuclear Power Pla n t. The values specified in the criteria for unconfined walls are one-eighth of the values specified for confined walls and this coriservative estimate based on judgment is considered to be reasonable.
13
l 6 REFERENCES
- 1. Mayes. R.L. Omote. Y. and Clough. R.W.. ' Cyclic Shear Tests of Masonry Piers, Volume 1 - Test Results.* EERC Report No. 76-8, May. 1976.
- 2. Chen. S.W., et. al.,
- Cyclic Loading Tests of Masonry Single Piers. -
Voluma 2 - Height to Width Ratio of 1.* EERC Report No. 78-28. Dec. 1978.
- 3. Hidalgo. P.A.. et. al.. " Cyclic Lead lng Tests of Masonry Single Piers.
Volume 3 - Height to Mdth Ratio of 0.5.* EEPC Report No. 79-12.
M ay, 1979.
I 4
I l
l l
l 14
@A M' C 0, B"x3/4"SQ TUBE BE AM SOFT SPRINGS (IK/ INCH)
$ THOMSON BEARING !: i Y & ROLLER VV I ~
STIFFEN TOP WF BEAM (ADOED)(Wl4al51) i _ _ i [ TOP WF j-BE AM (ORIGINAL)(Wl4 x127)
ACTUATOR 450 KIP C APACITY f
o i o I I I I I I C o l l l l (SERVO JACKS)
H m
HINGE #
/./
L1 l l l l l LOAD CELL CONNECTED TO REACTION FRAME
~
/ _L_
l l
SPECIMEN I I l
I (IO"xIO"al/2" COLUMN TUBE BOTTOM WF BEAM (Wl4x127)
HINGE N 'l l l l l g
\I l l l l I
n f-CONCRETE BASE BLOCK
/
3__4 I I -1 I I ,.1.w /
FLOOR LEVEL / f AXtAL FORCE
~yyyy u gyggf gjyyy ELEMENTS (2 WBx 3l) 77pyy- gggy I s jfyggf gytyy PLA W TH (" TIE-ROD REACT FRAME h3gg gEYS (TOP AND BOTTOM)
PIG. I SCIIEMATIC II.LUSTRATION OF SINGLE PIER TIST
L Cf n
i e
H/W RATIO - 0.5 '
STATE OF CRACKING - OBE STATE OF CRACKING - SSE !
1
, . . s .ss
' /*
s$v 'a j -
' )
/ -
\ '
' '-/y. i 25,. -
~
,\ .; '.f r
- C. %. 6..N8'i b:
4
~',;
.: ;m.; .
. . . . " ' J.t .if# g
. ....'^. m....
ac ,,y-]
c '.
- j N
< . . ~ . - . ;-i ," . ,>$
, ' . x 'Wj 'N47y ..?d 2N'
'h X)._k'AT[%3841 t ,
$ - ' ' ^
"Y d-s Th
^ - '
, ,t '- kb h Mb. Sta);e Sta);c .h ,[ . 'A E
- f,
._- u, n ., .
l W
. -e .
r . -
..p%g
- t.
- t. q. .
p 3 e N. 'f
!, ,?Y ,
.w s.
.x. g . ' ---+ ., .- _ ,
g' s - -
, a
?.A. '
'; -f N- '
Ef. 4- , % p' s p .,.'.
.s s 'y.*
- m- 9 "f - ',
- r r
., y..
d=
4 N
. a.s . .. . . . . .
\*
- g a, ,
I, ,. , , ie 4 s,.
. .C M, 4 _
g
.. . . A . , . g.R . ' 2~
FIG. 2 SUCCESSIVE CRACK FORMATION AND EXPERIMENTAL RESUI.tS TEST IICBL-12-3
I t
II/W R7.TIO - 1.0 I
STATE OF CRACKING FOR l STATE OF SSE IS STAGE 9 (Pi!OTO '
(
CRACKING - OBE IS STAriE 10)
. ~
%,. e <
~ '
, l I
y- ~. l ~1
) . ,
~
r- y y ..
r, \#
,6 i e s.,. o <
, - f
. t. ,
! , N
/. N 1
- l l .
1 i ,
+
._:., _.a__, '
I l
Lr,.,a u.. s ,
.. < - py .a l r
~al 5 A\ 9 axiu-a J~
,i y es- ' t- _ gr
_ Ef**
- d e - _
s ( ,,, ,- ,, ,.
% .e p ~.g .9~-V a--
, 1 T] . , ' . -
~
x_
,- -.} c .y .,.l - ,' ' % 7
-A>-,' y --,L:
N, 7 r; \j '7 ,
., ._ u. . s
- w. - .1 s .
j . ,- f ,. ( 4: \
\ .c .
.c
/a, . . . .
s,J
, g, - - -
g,-
, . Q . ,. ys---. 3 . \,- _
' 3
,b f, - .
f f 8 fin j, i.,
. .b 5 L u _, . .Ib ., ,
!_m_l..dJN
~
.a l . .
. ~ 1 m
T
.ga A- - - -
9 ya au_-
7.,Jo m a,.d s k
- a \ A,g,m
- u agw
_ _FNe ' 'i D_ ._ '_ . J2aar_ut e_
FIG. 3- SUCCESSIVE CRACK FORMATION AND EXPERIMSNTAL RESULTS m TEST HCBL-ll-4 17
. 4 H/W .%TIO - 2.0 ..
STATE OF STAT' OF CRACKING - OBE CRA(KING - SSE
~
ff .a A ? .t No e B E I i
l
- I j r !. l
.e g. , T
. I , I fpu j
ih ,
g t
[
, ? '.c L.
, ,, E ,' =,*
g , .
a 1. L ,
4--- + V E 0.e tC tiO %
+vt LATERAL C'SPL CommES '
SME AR F0mCE AN SatARSTRESS y e-
-VE Laf EN AL DISPL ComagS %' ., ,
y,4 p Sat AR FCRCE 4%C S=t AR Stat $$ $' -
- -- M*.1A O.16"; 23.O KIPS 0.29"; 18.8 KIPS 0.32"; 19.9 KlPS 12O PSI 98 PSI 104 PSI O.13"; 20.1 KIPS O.18"; 21.7 KlPS 0.24"; 19.1 KIPS 150 PSI 113 PSI 99 PSI
.. cy 4W". ;- .
l
-s?[E5 t .- . ,- ~, E i = ~; h ;
=- . 'MLIE8 tD+,. M* .?- f f-[,$NSC.dM.
- l p
' a =
g ., .
l
~
, II- .
)g b ..
s [J ?
, i a
a m llb
% ./. .o O . . .,x, R lL i ,
c y 'q y -
l
" a g_,' -
- ~~
9 + /tf1.N; 4 . a.' . ' Yia 1..
' Nt2F3 W.T1r.':rw;r. ,y. ... . .
5i
.(
O. 37"; 19.9 KlPS 0.51"; 10. 5 Kl P S 0.7 " I" 104 PSI 55 PSI O.28"; 19 KiPO O.41"; 13.6 KIPS 0.7 " I" 102 psi 71 PSI FIOUE 4 SUCCESS!VE CFACK FORMATION TEST G. (RIGliT SIDE P1CE) 18 l
- - - _ . . . . _ _ , . _ _ ~ . _ _ _ . _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ . _ _ _ . . _ _ _ _ _ _ _ _ _ _ . . _ _ _ . _ _ _ _ . - _ _ _ _ _ _ _ _ _ _ _ _
1
. % l G:mma DI:tributions: OCE & SCE i A , i Frequency I mean 0.00202 i 1
s std. dev. 0.000825 ' l 10 '
N <
/ \ Gamma (k = 6, A.2970.3) 8 ,# g
\
/ \
\
6 [' \
g l
\ ~
\
l 4 ' \
/ 's 2 / \
/
,r N %g
_/ l 'w % _
p 0 5 10 15 20 25 30 35 40 45 g4 Strain l
Em0.00202 OBE STR AIN DATA A
i Frequency r ,
l h mean 0.00318 10 < >
f std. dev. 0.000959
8 f
Gamma (k 11, %s3459.1)
! s~~
6
,i s/\
/ \
/ \
\
4 / s
/ \'
/
2 ,e' s\ s l s
/ \
- ~
m a r 4
( 0 5 10 15 20 25 30 35 40 45- 50 55 16
! Straini l
x = 0.00318 -
l SSE STRAIN DATA . . _. .;, . ;,,
l l
FIGURE 5 DISTRIBUTIONS OF OBE ANL S8E STRAIN DATA l \ 19
_ _ _ _ _ _ _ _ . _ . _ _ ._ _ _ ._ __