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Green Creek landslide

(2)

NATIONAL RESEARCH COUNCIL

esawaa

DIVISION

OF

BUILDING RESEARCH

THE GREEN CREEK LANDSLIDE

Internal Report 246s. 309 sf %he

Division of Building

R e

search

OTTAWA January 1 9 4 5

(3)

P R E F A C E

F o r a number sf y e a r s , the Soil Mechanics Section of the

Division of Building Research

has

been engaged in the study of the

g e o t e e h i c a l properties of L e d a clay. These atudie s have included $ha documentation sf c a s e records sf Handslidee.

One of the landslides that has been investigated is

the

"Green Creek" landslide, located on t h e eastern outskirts of the

G i t y sf Ottawaa. ATthough the landslide scar is relatively old, It has many of the characteristics sf the eart'lab%sw-type 05 1mdsli.de

that occurs frequently in Leda clay.

This

report s u m m a r i z e s the results sf several years sf work, It was prepared by D r . E .

L.

Matyas of Carleton University while

he

was engaged as a s u m m e r professor by the Bivfsisn.

Ottawa

January 1965

Robert

F,

Legget

(4)

THE

GREEN CREEK LANDSLDE

This

report d e s e r i b e e the r e s u l t s s f a study of the G r e e n Greek landslide n e a r Ottawa. Laboratory and field data have been included far completeness but have not been discussed in detail. Emphasis has bean placed on a stability analysis of the landslide site; in p a r t i c u l a r , a slope

Iseated west of the landslide crater. The apparent factor of safety of this slspe is in the order of 2 . 5 , E the actual factor s f safety is close

t o unity (the original slope in the slide area would have had this value) it

will

be n e c e s s a r y to r e v i s e the normal interpretation of parameters for s h e a r strength and pore pressure f o r the soil at this s i t e ,

An investigation of the Green Creek landslide has been carried out intermittently since 1958 by the Soil Mechanics Section of the Division of Building Research, National Research C ~ u n c i l , in order ( 1 ) to study the general properties sf Eeda clay, ( 2 ) to document the earth flow as a cPassical example of this type of failure, (38 to a s s e s s the theoretical

approach for predicting the stability of slopes, and (4) $0 determine the nature 0% the ground water movements in the a r e a . T h e Hmvestigatisn

included field tests and laboratory tests on soil

within

and outside the slide area and a stability analysis *airas m a d e for a selected slope lneated west of the 'landslide c r a t e r .

HISTORY

OF

THE L A N B S L D E AND TQPOGRAPMC FEATURES

The G r e e n Creek landslide is located approximately one mile e a s t 0% the mtawa city limits and about 508ft north ~f Montreal Road

(Highway 17) as shorn i n F i g u r e l o The slide w a s noted initially in 8a.1458

on contous m a p s which had been prepared f r s m aerial photographs taken in November 1957. Figure 2 , a contour map of t h e slide area, shows that the earth flowed in a northerly direction affecting an area approximately

1700 ft wide by 2800 f t Iongo that is, about bOO acres; the crater itself covers about 35 acrea.

3g Suaxnnaeac- P r s f e a s o r , Soil Mechanics Section, Division

QP

Building R e s e a r c h , National Research @rsumciP, Qttawa.

(5)

No r e c o r d of the earth fl.sw i s h o r n to exist and it is t h e r e f o r e almost c e r t a i n that the slide s c c u r r e d before the land was settled about

1840. Judging f r o m the appearance of the slide it i s probable that it o c c u r r e d the l a s t 206, o r 308 years.

VANE TESTS

In

the fall of 1 9 5 8 , a number of vane boring8 w e r e m a d e a% the leeations s h o r n im F i g u r e 2 - B ~ r i n g s ~ designated VS-H t o V S - 5 Hnc%usive, w e r e made on the slope located about 600ft west of the c r a t e r . The

boring% w e r e extended t o depths s f about 47 t o 7 3 f t where refusal w a s m e t . The r e s u l t s , given in F i g u r e 3, show that the undisturbed shear s t r e n g t h generally d e c r e a s e d t o a depth s f about % s f $ and then i n c r e a s e d , indicating a drying crust above this level. Somewhat lower s t r e n g t h s w e r e obtained in bssimga

VS-1

and

VS-2.

Following the initial t e s t , the vane w a s rotated rapidly through 25 revslutions and the shear s t r e n g t h of the rern~uldled s o i l was obtained. Sensitivity, defined a s the (undisturbed s h e a r strength)/ (remoulded s h e a r strength) i s plotted against depth in F i g u r e 4. %"&Hues range from a minimurn sf about

9

t o a maximum of s e v e r a l h m d r e d . In t h e s e t e s t s , a. 4-blade vane measuring 43 by 8 6 mm a s d e s c r i b e d by Andresen and B j e r r u m (1956) wae used.

Three vane borings, V G - l to V @ - 3 inclusive, w e r e a l s o m a d e in 1958 at the l i p of the slide in o r d e r t o d e t e r m i n e the nature and

c h a r a c t e r i s t i c s or" the m a t e r i a l involved in the slide and also to detesemline, if possible, the depth t o the original ground s u r f a c e . The t e s t r e s u l t s , plotted in F i g u r e 5, d o mot show any marked discontinuity at depth and t h e r e f o r e cannot be used to locate with certainty the position a% the original ground surface. A. slight disesntinuity is apparent for borings

VG

-1 and VC-2 a t a depth sf 25ft which corresponds to an elevation s f about 190ft.

Vane hole V X - I was made i;z undisturbed ssPP a f e w hundred f e e t south of the c r a t e r (Figuse 2 ) . The r e s u l t s f r o m t h i s "enale, plotted in

F i g u r e

6 ,

a r e reasonably consistent but somewhat lower than the strengthts obtained in boringa

VS-l

and VS-2. T e s t s w e r e also conducted s n remoulded soil and t h e s e indicated very Isw s t r e n g t h s with many readings of z e r o

which would sargga st sensitivity value s of infinity,

h

1960,

two additional holes, $PA-4 and VA-5 w e r e located on the apron of the slide at the locations s h a m in F i g u r e 2 , Again, these

holes w e r e made to investigate the p r o p e r t i e s of t h e disturbed s a i l and t o locate the original ground s u r f a c e .

h

both holes, o b s t r u c t i s n s w e r e encountered at depths of about

I 4 A

and some sand and w o o d adhered t o

the vane casing when it was removed, T h i s suggested that the original ground level w a s probably at this depth. Vane t e s t s w e r e taken between

P O

t o

6

ft and t h e s e a r e plotted in Figure. 5. These show r e s u l t s s i m i l a r t o those f s m d in borings V C - 1 , V C - 2 and VC-3.

(6)

The final vane b s r i s g , designated VX-2, w a s put down in the barnyard of SorPey" f a r m t o d e t e r m i n e whether water seeping through

manure piles and into the subsoil had any effect OR the shear strength.

The

r e s u l t s s f the t e s t s a r e plotted ic F i g u r e

6

and it can be seen that the r e s u l t s compare closely with those in baring V X - % which was located

some 600 8% f r o m the b a r n y a r d .

'The vane bsrinags a r e summarized in Table

I.

WATER TABLE AND P I E Z B m T R I C LEVELS

1x1 o r d e r t o c a r r y out a stability a n a l y s i s En terms of effective s t r e s s e s it i s n e c e s s a r y t o determine the p i e z o m e t r i c l e v e l s in the sub- s o i l . Since the stability analysis was m a d e f o r the elape west 0% the

c r a t e r , the determination of the water bevel and the pie s o m e t r i c level w a s concentrated in this area. The w a t e r l e v e l s noted in vane borings

VS-B

t s VS-5 a r e given in Table 11, These show that the water table at

the top of the slope was about 5;ft below the s u r f a c e

a d

n e a r the toe of the slope the water table was close to the s u r f a c e .

In

1961, three p i e z o m e t e s s , designated a s Nos. 17,18, and 19, wese installed at depths of 20,40, and 6 6 f t respectively at the location

shorn in Figare 2. In plan, the pieaometere w e r e 4 f t apart. Readings have been taken periodically since the installation and the r e s u l t s are plotted in F i g u r e 7. T h e s e indicate peak pieeometric l e v e l s in May of each y e a r and minimum bevels in August o r September. The level f o r piezometer No. 17 fluctuates considerably, since it i s closest t o the $roar;nd s u r f a c e and is m o r e subject to seasonal variations.

SAPPAPLIB?@ AND TEST RESULTS

In November P 958, a boring designated SX

-

1 , was made at the s a m e Iocatiori as vane boring VX-l. and undisturbed s a m p l e s were obtained

$9 depths s f about 23 ft. In October 1960, bsringa S X - 1 A w a s made c l o s e

t o boring

SX-1

and s a m p l e s w7ere taken from depths s f about 24 t o $Oft.

The

r e s u l t s of ~Hasaification tests, w a t e r cantent and density determinations, me% cansolidation tests are given in F i g u r e 8; borings

SX-

1 and S X - I A have been inclrzded in the profiles. The t e s t s indieate that the clay h a s weathered t o a depth of about 2 8 to 25f-t.

Cansolidated undrained triaxialb t e s t s w e r e carried out on samples taken from boring S X - 1 A . The grouping s f t e s t results f r o m an a r b i t r a r y number sf sampling tubes l e a d s t o a csnsiderable variation in the effective s h e a r s t r e n g t h p a r a m e t e r s c 0 (cohesion) and eq@ &angle s f i n t e r n a l f r i c t i o n ) as shown in. F i g u r e

9.

T o obtain an over -all average which would simplify the stability a n a l y s i s , all the r e s u l t s wese included on one plot (Figasre 10).

1

In

this plot, values of

-$

( 0

-

0 ) are plotted against 2

(01

+

0' ) T h i s

(7)

method avoids the

plotting

sf

numerous

~ W s h r c i r c l e s

which tend to

obscure

the

r e s u l t s . In

addition,

a

method

s f

least

squares

can

be

used to obtain an average failure envelope

through

the points.

T h i s

plot does not

give c%nd ~9

directly

but

these

values can

be sbtained

readily

by

the simple expressions given in Figure

10 [Bishop et al,

1960).

Using

this

method, the shear strength param-eters

in

terms

of

effective stresses

were

found to

be c" 6608 psf

and

q Q

= 1 9 . 2

degrees.

M a x i m u m deviator stress w a s cansidered

as

the failure criterion.

Two

borings designated

as

SA-4

and

SA-5

were m a d e

adjacent

to

borings V A - 4

and

VA-5

respectively

in

September

1960. Some

tests

were

carried om%

and these

a r e plotted in

Figure

HI. In

both boringe,

organic matter

was

noted at a depth of about 15 to

17

ft

which indicated

the original ground surface,

This is a l s o

confirmed

by the discontinuity

in the water content

profiles.

STABILHTY ANALYSES

Since the original profile

sf

the slope affected by the landslide

was

not known, the slope

located about 6 0 0 f t

west sf the crater w a s

selacted for

analysis;

the location

is

shown

in

Figure

2

and the profile in

Figure 42. This location

w a s

chosen because:

( 9 %

the gradient

is

relatively steep

and

constant

and

therefore

it

can

be

assumed that

it may

be the most critical

slope

in

the

immediate area;

6 2 ) it

might

be assumed

that

t h e

gradient

of

the

elope in

the slide area

was

similar

$0

the slope

baing considered; and ( 3 )

if

the

slope

is at

Pimiti~g

equilibrium,

a

etability analysis should give

a

factor

of

safety

sf

unity

provided

the

csrrect shear strength

and

pore pressure parameters

have

been used.

T o

carry

aut a

stability analysis

in

te1~1-n~

of

effective stresees

it is

necessary

to know

the

ground

water flow pattern.

O n the basis sf

limited information an approximate flow

net

w a s sketched (Figure

h 2). This

iazdicqted that the

flow is

nearly vertical,

%hat

is, th-ae

underlying

till

or

bedrock provides free

drainage

with respect

$0

the overlying clay,

The stability analysis becomes m u c h

easier

if an average

pore

pressure

ratio, r

can

be

used:

C$

r = -

u

Y

I-3

whqre

p

is

the:

pore pressure expressed in beet

of

head,

Y

is

the

unit density

of

the

soil,

H is

the height sf overburden in feet.

A n average

value

w a s obtained by drawing

a

few

trial

slip

u

(8)

w e r e then averaged arithmetica%%y to give a value sf about 0 . 2 0 which

wae used in the analysis.

O w the basis of reswlte obtained from t e ~ t s on 8ampEes frorn boriags SX-h and 5%-PA the following values w e r e a%sa used in the analysis.

y - 1 O O . O pcf; e b = 608 psf; r g 8 = 1 9 , 2 0 ,

Using

these values, a number sf t r i a l s l i p circlee were d r a w n and analysed. It w a s a s s u m e d that the failure was deep-seated, that is, the failure a r c s were tangent t s the underlying hard stratum. A few

shallow c i r c l e s were also analyaed and these gave higher f a c t o r s of

safety. O n this basis sufficient c i r c l e s were analysed ts locate the c i r c l e having a minimum factor of safety. This circle is shown in Figure 13; i t had a factor of safety of 2 . 4 % .

The calculations were made with the use sf the Nationah R e s e a r c h GornnciI8s IBM 1 6 2 0 , M a r k I1 computer. The program for the computer w a s prepared in F O R T U N

I.I

and reported separately by Irwin (1964).

Briefly, each circle required a separate data card which included:

%

-

the x cs-ordinate of the centre of the c i r c l e ,

8

Y

-

the y co-ordinate ~f the centre s f

the

c i r c l e ,

0

W

-

the radius of the c i r c l e ,

$b9

-

the n u m b e r of the c i r c l e ,

S

-

the

number of d i c e s ,

XS

-

the x co-ordinate s f the c i r c l e a t its interseetihsn with

the top of the shape,

XF

-

the x cs-ordinate of the c i r c l e a t i t s intersection with the bottom s f the slope,

TOT

-

an estimated f a c t o r of safety.

Each slope was csnverted to a number of straight-line segments, The number of s l i c e s was a r b i t r a r i l y calculated by dividing the c i r c l e into slices about

PO

ft vride. Fsr a typical c i r c l e this resulted in about 25 slices.

Initially, an estimated factor of safety of unity w a s used; a s the

actual factor sf safety was over two, the e~mputakiomr time par c i r c l e was ae much as 10 minutes.

The

p r o g r a m was later streamlined and a m a r e

(9)

time per circle to l e e s than a minute in m o s t c a s e s

The method of analysis was by a method of e12ces p r o p ~ s e d

by

Bishop

(1955).

It w a s obvious that the value

sf

2.4'7 for the factor of safety w a s eoneidarabPy higher than one might expect for a elope located so close %a an area that bas actually bailed. This discrepancy can be attributed to

several factor a:

(a) The initial slope of the clipped area is not known and it % e

possiblle that it was steeper tkqn

the

adjacent slopes,

($1

T h e value used far the pore pressure ratio

r

was too Sow, u

( c ) The shear strength parameters as interpretaa were t o o high.

Of

these possibilities, there is ns way to check (a) but bath

(b)

and (c) m a y be changed. There does not appear to be any $nstifica%ion

for changing [$) owing to the measured pore pres<suree. Nevertk%ehessg

other values

of

r ,

w e r e introduced into

the

analysis. This only required recalculation for the critical circle since a change in r, only d o e s not affect the position sf the critical c i r c l e ,

As

seen in Figure 184 a m a x i m u m psseibke value Ear r, of about 0.

6

only reduced the f a c t o r of safety to

about 1 . 7.

Figure 9 indicated a large variation in the shear s t r e n g t h parameters

when an arbitrary grouping sf the test results w a s considered. Crawford

(1961)

has also shorn that different va%ues

sf e g

and

as

can be obtained from

one s e t of test reau%ts depevlding on the method of testing and interpretation,

On the basis of these arguments there is some &stification for changing the shear strength parameters

.

Hence, additional analy a e a were m a d e to determine the effect a% variatisn in cohesion and friction sn

the

f a c t o r of safety. A change in either et or q%ehangea the position of the critical circle.

The results are plotted in Figure % 5 and these indicate that when c B is extrapolated to zero

the

apparent factor of safety still exceeds unity.

The possibility that c E decreases with gasPogica1 time Baas been recognized

for s o m e t i m e and this has been confirmed recently by Skempton (1964) who

has reported a number of case histories.

H e

suggested that m o s t soils have both a peak and a residual ekear stkength and

the

residual strength m a y be considerably less than the peak strength. This woa;ld not appear to be

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applicable to Leda cEax however, since it does not norm all.)^ exhibit a decrease in strength once the maxhmuzm eksmpreesive strength has been reached. There m a y be an analogous situation f o r L e d a clay in which the strength d e c r e a s e s withetime but this has not been formalatedo It may also be argued that the triaxiak t e s t does not simulate field conditions and the observed behaviour i s misleading.

It i s also seen in Figure 1% that the friction angle, rpB, must d e c r e a s e to a l m s s t zero bedore a factor s f safety of unity is approached;

such a d e c r e a s e , hawever, coeeld only be r e a l i s t i c if it can be s h a m that

the soil i s purely cohesive.

On the assumption. that s B can approach z e r o and ep8 remains constant at 19.2", Figure

I 6

illustrates the effect s f r,, on the factor of

safety, that i s , a value s f c" 0 and r, = 0. 3 3 will give a factor of safety of unity. This particular analysis was based on an equivalent straight- line approximation for the slope a s shown in Figure 1 6 ,

A s an alternative, the soil profile considered in the analysis

could be divided into four a r b i t r a r y l a y e r s and represented by the different shear strength p a r a m e t e r s given in F i g u r e 9 znd re-an-aalyeed, This

procedure, howe~rer, might also be questioned because the samples f o r shear testing w e r e taken from one boring located s e v e r a l h u ~ ~ d r e d feet from the ana1yae.d section and the assumptian of uniform soil prspertges throughout is %as% strictly justified. This argument may a l s o be extended

to include the effects of the different s t r e s s history imposed on the soil at the top and the toe s f the slope

.

Referring to the crftieaP circle s h e w in Figure 1 3 , it i s seen that a considerable portion of the circle passes through the upper desiccated

Z

5 to 20 ft s f the s t r a t u m , In addition, computations will

show that the effective normal s t r e s s along a t r i a l slip surface is ueual&ly Low and in this case does not exceed abeut 2 kgdcmZ. 2.n consalidated undrained t e s t s the normal practice i s ts t e s t samples a t high confining p r e s s u r e s in o r d e r t o obtain a straight-line failure envelope which can be extrapolated into the low effective stress range. With overconsokidated soils, tests made ia the how effective s t r e s s range, howeverl Cia not

appear t o give r e s u l t s that coincide with the extrapolated failure envelope. This has been recognized for some time and recently Crawford ( 1 9 6 3 ) and Crawford and Eden (1964) have reported some experimental evidence of this f a r Leda clay. This type of r e s e a r c h couHg9 be expanded to include t e s t s on samples taken f r o m the desiccated c r u s t .

A s mentioned previously, z %Bow net had been prepared from readings taken from t h r e e pieze~meters installed at one locatian. This necessitated the extrapolation of these observations to cover the fall

(11)

length of the s l i p c i r c l e . Additional pis eometera instalked a% s t r a t e g i c points f u r t h e r d o w n the slope would both simplify the csnstruction of the flow net

and

increase i t s reliability.

Tension c r a c k s had not been cansidered in the a n a l y s i s since it was thought that these would have a m i n o r effect a s the factor of safety. ACKNOWLEDGEMENTS

The

planning s f this investigation, as well as the s u m m a r i z a t i s n of observations and t e s t r e s u l t s , i s credited mainly t o M e s s r s . C . B. Crawford and

W.

9, Eden. Field and laboratory t e a t s involved, periodically, m o s t of the personnel in the DBR Soil Mechanics Section. The a ~ t h s r has collected m o s t of the observations and t e s t results in %&is r e p o r t and with the aid of M r . W , Irwin ( s u m m e r student) has used t h e m t o c a r r y out the stability analysis. The aid s f per sonsel in the $%RCes Computation C e n t r e

f s a l s o achowBadged.

REFERENCES

Andresen, A. and E. Bjerrktm, (1956).Vane testing in Narway, Symposium on Vane Shear Testing of

S o i l s ,

A.

S.

T.

M. S T P No. 1 9 3 , A m . Sac. Testing Mats.

,

p. 54- 60.

Bishop, A,W. (185508. The u s e s f the s l i p c i r c l e in the stability a n a l y s i s sf slopes. G 6 o t e c h i q u e , %Pol, 5, No. 1, p . 7 .

Bishop, A. W . , I. Alpan, G . E . Blight, and H.B. Donald,

fE960).

Factor e coratroPBing the s t r e n g t h of p a r t l y s a t u r a t e d eohe slve s o i l s . P r o c . A m . Sot. Civ. E n g r s . , R e s e a r c h Conf. on Shear Strength of Cohesive Sails, Boulder, C s l s r a d s , 1960, p I 583-532.

Bishop, A. SF%, and N. M s r g e a ~ s t e r n , { 1 9 6 0 ) . Stability coeffieien-ts f d r e a r t h s % o p s . G & s t e c h i q u e , Vs%. 10, No.

4,

p, 1 2 9 .

Crawford, C . B. (1

961

1.

The Inf%uemce of s t r a i n on shearing ~ e s i s t a n c e of sensitive clay. Proe. Soc. Testing M a t s .

,

VoE,

61, p. 1250-1276.

Crawford, C , B. $ 1 9 6 3 ) . Cohesion in a n undisturbed sensitive clay. GCoteehique, Vo1. 13, No. 2 , p. 6 3 2 .

C r a , w f ~ r d ,

C.

B. grid W. J . Eden (1964). A comparison of la5orator-q~ r e s u l t s with in situ properties s f Eeda clay. Paper submitted t e the Sixth

ht.

Con%. sn Soil Mechs. 2nd Fsundn. Engineering, t o be held in Montreal, Canada, September 1965.

(12)

Irwin,

W.

(%964), The use of

a

digitall computer $072 ~a1ving slope

stability problems. National

Re

seazch C smciP, Division sf Building Researc&Gomputa% Program

L9,

Skemptcm, A , W.

(B

$64). Long -term stability of clay slopes. G & s t e c h i q u e , V a l . 14, No, 2 , g. 77.

(13)
(14)

WATER TABLE

IN VANE

BOMNGS

(15)
(16)
(17)

S W E A R S T R E N G T H , K I P S I S Q . FT.

F I G U R E 3

F I E L D V A N E T E S T S , P R O F 1 bE W E S T 6F C R A T E R M52#Y-3

(18)

S E N S B T O M I T Y D E Y E R M l N E D B Y R E M O U L D E D F I E L D V A N E T E S T S . W E S T OF C R A T E R

(19)

F I G U R E 5

F I E L D V A N E P E S T S A T L I P A N D A P R O N O F 5 % 1 9 % @@ saw- 4-

(20)

S T R E S S , K B P S F S Q

FP

0 1 2 3 4

5

Q

F I G U R E 6 F I E L D V A N E T E S T S S O U T H

OF

C R A T E R 6?@3X87-6

(21)

F I G L I R E 7

(22)

T E S T R E S U L T S OF U N D I S T U R B E D S 0 F L IN B E L W f [ O M T O D E P T H

(23)

Green C r e e k L a n d s l i d e

F I G U R E 8 8

(24)

cA

(PI zi 0 0' PBI & Pad a. a k4 (PI m W az r- tA u >

-

i-- %a W t& bL W

(25)

F I G U R E 10

A V E R A G E D C O N S O L ! D A T E D - U N D R A I N E D T R 1 A X I A h T E S T R E S U L T S

(26)

W a t e r Content - % D e s c r i p t i o n 0 6 % &I84

0

.----

.-=_

Weathered Red Ckay wits Siit Pockets

Bet

.__ -- --

Gry Clqwltk Red Patches

_ _ _ -

- - -

-

- - -

~4

Grey Clay with Silt Patches

J - - - .

---

---

- - - -

I-'

Greenish Grey to Brown Clay

with Organic Matter Kirvigs) Ground Surface

W a t e r C o n t e n t - 9b

..zP

Q

20 4(9 60 80 1 , 1s.c.l B e s c r i p t i a n Weathered Brown Clay

h . 4

1 1

.

...+

(27)
(28)
(29)

R E L A T I O M S H I P B E T W E E R FW@%OW OF S A F E T Y A N D P O R E P R E S S U R E

W A B $ O

Bc'

-

600,

8 ' -

1 9 . 41

(30)
(31)

103

m

m

m

5m 680

C Q H E S l ON, c ' ,

L B P E R

S Q Fb

c' = 600 I& per sq fb

ANGLE OF I N T E R N A L F R B C T i Q N ,

PI',

D E G R E E S

(32)

Profife Used for - hL P O R E P R E S S U R E R A T I O . r, R E L W T l O N S H B P B E T W E E N F A C T O R OF S A F E T Y A N D P O R E PWE$SUWE R A T I O ( c ' = O F B i = 19. 2'1

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