CM SCALE f~R - nonlinear seismic analysis of arch dams

DEF~RMED

SHFWE

Cl~ ~ ^{. .}

"if\'1

) \co 'i~'i

"'H°'

91 CO~N

~111

r-1...JN

j~7

"'7 I ..

- y

CAN TI LEVER

co

DEAD WEIGHT + HYDROSTATIC Dead weight applied via a construction sequence.

"""' 0 .4 I

0 l

FtJACE AT NtJOE S

- - - - ORIGINAL CKJ

·-··-··· tOCRL CKJ

FORCE AT NOOE 35

s ·a

Applied forces and plotted displacements are in the

z

direction (approximately normal to the dam midsurface).

0 l

FORCE AT NOOE 3

- - - ORIGINAL CKJ

FORCE AT NODE 35

CKJ

9 8

b. Applied forces and plotted displacements are in the

x

direction (normal to the foundation interface).

Figure 5.7 Results of investigation to assess localization of [

.K].

Forces are applied at nodes 3, 15 and 35 on the foundation interface, and the displacements are plotted around the interface. Each displacement profile from the original [

.K]

is normalized to a peak value of one and the scale factor required is also used to scale the corresponding displacement profile from the local

[.KJ.

Figure 5.8

0 8

13w u en d: t.U

14u..o XC d: :z:

t-40RMRLI~EO 0

FORCE

a. Acceleration of node 12.

1 l

N~RMALI1EO

FrlACE ^tl

- - - - CIRIGINRL CK,.,J --- L Cl CA L CK,.,J

b. Acceleration of node 31.

Results of investigation to assess localization of [ Kpp]. Applied accelerations and plotted hydrodynamic forces are in the

z

^di-

rection (approximately normal to the dam mid-surface). Each hydrodynamic force profile from the original [ K

PP]

is normalized to a peak value of one and the scale factor required is also used to scale the corresponding hydrodynamic force profile from the local [ Kpp] .

Figure 5.9 a to j (next 10 pages). Summary of the earthquake responses of Pacoima Dam t~ the records of Figure 5.1 scaled by 2./3.

Results for both the partially full and full reservoirs are pre- sented: static stresses, maximum tensions for linear analysis, maximum openings for nonlinear analysis, and maximum compressions for linear and nonlinear analysis. Stresses (MPa) are shaded with amplitudes given to one decimal place. Openings (cm) are unshaded with amplitudes given to two decimal places.

11'

})-"~'\·"

LINEAR ANALYSIS

~# "*

~

^~:t- 4.02 5.H 2.11 't,.

2. ol l I ; I I, I~

\•~\ ~?11

^l.H

!.fl~ ~ ...

...

,.. '·•

fl/ •

'~ ~·

MAX. llPENINGS

~~~

ti ~~{ti·•~ NllNLINEAR ANALYSIS ~~,~ ~ ^...

W '

^/~ G -U· I -12.1 -II. s -'•

fJ {. -\"" ~~~ .... ~

.,,. A•"' ~ 4 2 -4.2 -4.t ~ ":"1.₁

., ...

^~...

.. ..

t:.' <C' ,~ ~' MAX. CllMPftfSSiaNS .... , ~

()' :-.·Y _/>·'\

LINEAR ANALYSIS

"-•-....::..'\....,,.o

,~~.. #;,'\'"'

;;/:

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-'I.'·'

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-\S• -1~. a

. . .

~-~~~?

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v,,

-~"

f>' <13':

(#~·'" ~

MAX. COMPRl!SSillNS

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~ ~ ~~~

~

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^,.,.

..."'

... ";>

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....

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(:I ~//'\•'\ LINEAR ANALYSIS "-• ~

.... ~ .r ~·>

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,. •' :::l±'

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.

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.,.. "'

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MAX. OPENINGS

~...:~'*

11° -.'//~'" NONLINEAR ANALYSIS ~~ 0. >

~~.,

,,

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{ff

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MAX. CDMl"RESSIDNS

~ ~

~ ,,.;("(_..• LINEAR ANALYSIS ".t~~ ~_,.

~

^,/p,· ^.1.4 -a.s 0.1s ·~

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:s:::-

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r.t'... \\~ ... ,

-% ..o.•

-l.7 ... ~

1.,.

,,. r •• ~ I~.?

~·

^t:.':

,~

^{... '\} ^MAX. COMPRESSIONS

~ ~

1t·'// ,t.··

NaNLlNl!:AI\ ANALYSIS ~."'"'"

/\_.; oJ ·~

~

'/fl//,'...

..,,.

'l:i '"

~ ~

.

t:.• c:.

'JI'

Figure 5.9a. Arch 0 (ground motion scale = 2/3).

... I

00 0

[J'-JTj~I_J []'-J-r_j·:I_J

oti' .... ~ ('I)

CJ1 - - - -0.1 - -0.9

-a •• - -1. a ^-1.a

-a.•

^- ^- ^-0'1 ^.

(o ^{-1. I} ^{-1. I} ^{-l. S} ^•

O' STATIC STATIC

-2.6 0.5

fl" ^-1-:11:1?

^- ^- ^,,9

^r~·

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^- ^-

^__:11·:

¹ ^2.0

^T._J

Q 2. 1 - 1. 1 2. 2 '· 2 -1. 11 -1. 9 O. '1 •. -0

~ ::0

:::s MAX. TfNSIDNS. LJN!Aft ANALTSJS "AX. TENSIONS. LINEAR ANALTSIS ^::0

.,... _{- t}

....

;"' -3. s 0.,

....

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- 1.

i::: o. ,., ^{1. •} a.• • -s. ¹ -s. ^I. 1. 1 •

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p.. HAX. OPENINGS, NONLINEAft ANALYSIS

-

^Q NAX. OPENINGS, NONLINEAft ANALTSIS

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^tn

s

₀ ^-0.9 ^::JI ^{..(I • •} ^,.,..^:JJ

L1._ll:t=T._J _[1'

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e.

^- ^- ^-2.9

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II HAX. COMPRESSIONS, LINEAR ANALYSIS MAX. COMPRESSIONS. LINEAR ANALYSIS

t-.:i

---

^c,.., ""'· 9 ^..(I.^l

[1 [~l~LJ;T._J

..___..

-1··t:ts

-u.1

o.ss- .... s -s . ., -s.a ..,,.,- ""'·" ... ...1

MAX. COHPftESSIDNS, NONLINEAR ANALYSIS "RX. CDMPftESSIDNS. NONLINEAR ANALYSIS

~~ ,..~ MAX. TENSIONS $,? ~~i'

~

^-. LINEAi\ ANALYSIS #../ ~ ..

; . ... ¥

1. 4.1 1. 75 '· co ~

... ~ ^Q.⁹⁸

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J)".)/"'°O •

NONLINEAR ANALYSIS

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^~"'O. • 4'

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.... i" ~ ..

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00

^~~'1. LINEAR ANALYSIS ~.)._~'Ir.,.

'" -1.\·0 -1a.o -1a.o

er.(

" ' / . ft.• o-~' ,.-:~

r.:: -..,

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,~·· ~:-

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.... r-2.2~a-Y..~....,.,

_0.&t~ _..

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~

^o•~ NISNLINERA ANALYSIS "lq ~ ..,, ..

w ~ #~ ~~

~ ~

~

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^..

;- ~

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p ,~ ~ •

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^L ".> LINERft ANALYSIS ".)l,"'-

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^:19

•. v"/ A~°' ~n.t1D.

^920.

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p; , / \• 1.1 l, If "./

,,~ \ • · MAX. DPENINGS '·ct ~

~ / Y ~ ~

~

^{/ ' •} NONLINEAR ANALYSIS

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~/ o-

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_.... .,()

_...

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^\ ^..a.

^ro. ^a--;,

^{2 -}

... -i' ~o."

~~ ^/ ^:;_i...G MAX. COMPRESSHNS '#.•

;;/:<.

,.~~' LINEAR ANALYSIS ~,~ ~~~

• -1.0 -1.8 -?.f ^A

.-.6'r

!'~ Pl' .... 0 ...-

:1:"':

.... ,

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-,.

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~

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~

,...

^' ~ ~/ ()

~

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;:~ .... '?.,"

~· _,..,.

...

Figure 5.9c. Arch 1 (ground motion scale = 2/3).

I I-' I-'

er'

1.1· - = J_-i ^::r~ ^J::J 1.1· ^- =J_l)~J::J

~· .:

.,

('I)

c.n -0. I -1.1 -0.I -1. '1 -1.. -a . ., .

(o _~ STATIC STATIC

1.1· _ =1_L2':J? ^I. 1=1--1-:t~ ^T.-1

Cl ^1.e ^a.a ^1.1 -a • ., o. 1 1.1 "11

Pl "AX. TENSJDNS. LINEAR ANALYSIS MAX. TENSIONS. LINEAR ANALYSIS ^:IIXI

::s ...

....

...

""

^XI

~ l.l!_1LLt~-1

^c:^r

1.1-1-r~"-T-1

^r^r-

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"'

^- ^- - - 2 . 4 r-

.,

1.s 2.2 2.1 ^::D_< -s.e -4.7 2.s ::D

0 MAX. DPENINGS. NDMLJNEAft ANALYSIS ^Cl "AX. DPENINGS. NDMLIMEAft ANALYSIS ^I'll

s::

-

^U)

::s :a

"'

~ :u

s

⁰^c+

^...

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1.-1-1-r

- - - - -

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^-_T-1

^-2.9

^r.-J• _]=l~J.;T.-1

^Cl

^-

^:II^<

-S.I -4.B -4.S -s. I -S. & -S. 0

Pl (D' HAX. ca"PftESSJDNS. LINEAR ANALYSIS MAX. CDttrftESSIDHS. LINEAR ANALYSIS II

1.1~1-i~"-~ 1.1-1-r~·"-y-1

---

._,

X - 2 5 . 2

J.:-s.o

- - - -9.7 - - - -I.I

-4.2 -4.8 -4.7 -t. s -4. a -4. a

"AX. CD"PRESSIDNS. NDNLINEAR ANALYSIS MAX. CD"PRESSIONS, NONLINEAR ANALYSIS

~

"' °'.•

"AX. TENSIDNS f. I "::... 't>

,,_.~,?

LIN•AR ANALTSIS • • •

~·

"' " o.. sa a. ao ¹ • / - : . .

... A·

--r-r -·

^o, ^.,. ^••

~ ^.. ^~· ^-u-:r~·

^'!'

~ ^{.. ~} ^~- r-o. ;-./.- ('"I.,, "

:~

^0·" ^• ^0.

~ ^/vfl6 MAX. llPENINGS • '.t ~ ^..

~?'/ _~

^.,,!'• NONLINEAR ANALYSIS '· /1

,(<,'.fl

-1.t -I.I -: o

':'.

o-~ ~I .,. ,

^.to

^v:1·'b

<)'

_~>. ~ 1' Io." _~ -:

' ' \

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MAX. CDMPRESSIDN;>.ci

L°'l:_' ^~

.._,

, : (

_~ _~· ~ .,,~ _' _~"· . _...- ^...

LINEAR ANALYSIS

_-.-- ^.... _-. . . ^_,

">.,

^... ^·~ ~q ^~ ^.

> ,. ,.... .,,

-;;J ~

~~

•·"" MAX. TENSHINS

'·:t ( '

i" ^.,."' LINEA ^ft^ANALTSIS )-.. ^••

(',q

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^·"

~-~'

^{} .}^...

^..!.[.s ^_-11.. ~.,. /~"'

~ ^~

^- ^-

^{~ ~IP}

~ ~ "' •·' ... .r.-ff ...

!"~

^{/\·· ..} .. •• , ••••

~:. ll.. ('.

I' ^v'> NDNLI NEAR AHRL TS IS

>

•I

<'-

^1q

... ~ _~ " 1..1 ~ _~- I-s.. ^-=-2·. _{~· ~·} ^.,.,. ^,;.,.

.. x- ~ ,. ... -... -.fr ^~.

q"I>

~1 ~<>' ....

CDMPRESSl ... r ) ' . •

~ v.,..

LINEAR ANALTSIS

~ x

,,· "

/>".

~·· ~ J_. I ....

^o ^...

~.. \:!~ .,,~,, ^{• /}

.. x- \-. ... -... Tr ^~~ ..

' } ' J:_)_ ^•Cl '>

~ _ ,.. ... T--,:.::.£. ·,

~ ^,*\•"

MAX. COMPRESSION:•.,

~

~~-<.. ~ _~ ,...,.

NONLINEAR ANALYSIS ">.•

_~ ~t> _·~

. _...

•

Figure 5.9e.

"'(y. ~<Ji··

^MAX.

COHPRESSIGN~.t~

⁽⁾

>•

NOML I NEAR AN ALYSIS "( # ( ' _ "

• ...

rch 2 (ground

^m~oo

. 1" ^scale= 2/ 3)

^. '~ ~ ^,,>

^{/ '}^•

....

~ I

"rj

l_l~ J ^l ^J.~ r_J l. l!_ ^J-r ^~- ^·-y-__.J

al:j'

] _ -0.1

.,

- - - - -o.s

(I)

Ol -o.s -1. 1 -a.a ^{-1 • .,} ^-1... -o. 7

~ STATIC STATIC

:-+>

f.J~J_LTT._J l. ]-J L ^1': ^:r_J

- - a.1 -1.2 - - - 2.1

l. l 1 •• -a. 2 a.e 1. 1 ^{\ I}

() ^D

MAX. TENSJDNS. LINEAR ANALYSIS MAX. TENSJDMS. LINEAR ANALYSIS :n

~ - i

::s

-

c-. l.1~ J _~ 1; ^;r.:J ""

l.J-l-J1_£·-r_J

^XI

iii" ^c: ^r

< ^r- ^r

ti> r -< I

.,

:JI "'11 ...

. ] ... -a.1 ...

I--'

"'

^c: ^w

-

^()(I

.,

_1.1 _2.1 _-4.1 ^UJ

_"'

:JI ^- -a. I ^- -4. D ^- -a. I ^_.--I.I ^r^r ^I

0 < ^:JI

~ "AX. GPENIHGS. HDNLJNEAR ANALYSIS ^a "AX. DPENJHGS0 NaHLIHEAA ANALYSIS

"'

::s ^p..

-

^:JI ^(J)^1'11^:JI

s

⁰^c+

l.1 - =tl_:[T._J r.1~1-11::r_J ^....

^<^a^:II

...

0 ::s

t/l (I

~ -4. s -a. ⁰ -s .• -s. ... -s. 1 -2.1

iii"

MAX. CaMPftfSSiaNs. LINEAR ANALYSIS MAX. CO"PAESSIONS. LINEAR ANALYSIS II

t-.,j

f.1-llTR l.1~1-1~·· -r__.J

---

....__..

] _ -2.1

- - -10.2 _ - - - -S.6

-4o. 2 -5. 2 -4. SI . -4o.D -4.2 -S.5

MAX. COMPRESSIONS. NONLINEAR ANALYSIS MAX. CGMPftESSIONS. NONLINEAR ANALYSIS

FULL RESEAVl:UA

~ '\ ~·" A-·' ... ~ ... ^fl:t

" ~· '}/, 1,,!" I .._!1' ~ ^p•

t:f/ ,,.

i 1 L !.';-~ ;,LJ..~: ~ i 1 kt·~a ~ ;h~ ttl ;; ⁱ

1 L .; ! ~

ff

^I ^{/ ;}^:i ^::! ^/.:

^~

^a: ^t:I ^:;

^~ ^'f.:; ^~

^a:

.. H ..

^. ^·:i

^~

H" ;;

^• ^{Z Z N}

^~ H"'

^• ^:l^{L e •}

^{~ ~H ~}

^I'- ^0..11:•^{i ..}

H

^•

^~

^O..c^I

'1\ ll:;;

N\ '1 ~a:..:\ ^Cf

a:' ^o ^I c'

^d ^I~

~\.J~ o\.J~ i ~ ~.\__.J~.: ^{; ; ..} \~~ ~ ~ .-.\~~ -~ i

,, '*· 1\

^\C" ^..J

~\

' " " z

-.\~

\C",S:

Vfr'"" \~.

^!IC ^z

·0:0·~·0<~:0~

0 'o • 't.. ,. 't... "C!t ~, 'o

Figure 5.9g. Arch 3 (ground motion scale= 2/3).

-·

..,

~ CD 01

to ::i-'

()

a

-· ~

..,

t-,:)

...-..

()'Q

a

::s p..

s

....

er

::s

Cll l"I Pl

CD"

t-,:)

----

^i:..:i

..__,

[

- -o . .,

- 1

-0.1

- -o.• ^{]_-a ..}

STATIC

[ _

1

^{2 . s _}

¹ ^_,_

1 _ _. •• _~_:J

1-

^-2.s

-

^{2. 5}

-

^{•• 2}

- ...

MAX. TENSIGNS, LJN!Aft ANALYSIS

[-1· - -. _-o.s--t[-_.l r

Lf _

^l.15

1..

- 2 . -

. •

2.11

MAX-_ GPENINGS, NGNLINEAft ANALYSIS

[-Or··-11=:r_J

_- _'-2

_.. s -4. I

MAX. CGMPft!SSIGNS. LINEAft ANALYSIS

[ -o.r·-1-.a···-~ _L-20.1

- --4.6 --4.0 -10.1

HAX. CDHPftESSJGNS, NONLINEAR ANALYSIS

..,..

c r

r :a

"'

:JI <

-

:JI

[-J'-J-o.s _-a.s_T_.J

j_

^-0.1

- -o.s .

- -1 ... : - -o.e STATIC

1 ^~].,

^{1 0}

I_ -J_J':T._J

- - 1 . 2.5

0.. • ..

MAX. TENSIONS, LINEAR ANALYSIS

[-]' 1

^- _ ] _ -2.s ^{-.:2. 6 -}

^.:I ^:J

- - 2.5

l. 2 --4. 2

MAX. GPENINGS, NONLINEAR ANALYSIS

[ J

^- ^-s.s

^'-1-J·•

^- ^-a.²^{- - s s}^{] _}^•

^-_J:-_.l

^-2.!I

MAX. CGMPRESSIGNS, LINEAR ANALYSIS

[

-0.'I

] _1., -.J.ll_r_.J

j_

^-2.6

-

_-4.S

-

_-4.S

- -s.•

MAX. COMPRESSIONS, NONLINEAR ANALYSIS

""'Q :0 :JI

...

:::0

r r

.,...

c: r r

:II

"'

:II <

... Cl :JI

... I

...

CJ1 I

FULL AESEAVGIA

Figure 5.9i. Arch 4 (ground motion scale = 2 / 3).

'- 1·-r_1~~_J [J·-1-~··-r_J

i:::

J _

^-0.1

Cb - ..,... - -o.s

'11 -0 • ., -o . ., -1.S -0.8 .

... ~ _STATIC _STATIC

[J'-J_-i:1.-_J []'-J_J~:.t_J

- - a., -s.1 ^- ^- ^2.&

Q a. D • o • ., 1. 6 _-0

pl "AX. TfNSIGNS. LIN!Aft ANALYSIS MAX. TENSIONS, LINEAR ANALYSIS :0 ^:D

::i -1

~ ...

-·

(D" ^"II ^:0

[ 1·-1-~.7~_J

^c:

[1-1~·"'-r_J

~ ^r ^r

'1 r -< I

t,,j "'rJ ^t--'

1-l.H

^::ll

J_

^-2,2 ^I-'

..--.. ^ITI c _--1

()q IA r ^I

'1 - - .... • 1.11 ^ITI - - - 2 . - i r

0 1.. • ^::II -2. 9 -s. 9

i::: < :n

::i MAX. OPENINGS, NDNLINEAft ANALYSIS ^ca MAX. OPENINGS. NONLINEAR ANALYSIS ^l"I

p..

-

^:u ^U)^ITI

s

^:n

[ 1= 1-:t ^1,-_J ^[1' ¹

0 Ci

~ - . --:'· o_

j'

^:..J

^....

5· ^:xi

::i

_ ] _ 2.0

rn ('l

pl - - a.a

-

^Cb ^{... 1} ^{... •} ^• ^-2.a ^-2.1

II MAX. CDMPRESSJDNS, LJNEAft ANALYSIS MAX. CDMPRESSIDNS, LINEAR ANALYSIS

t,,j

--- "" [1=1-r:r ^[J-11-r_J

..__..

- -2.s

- - - -s.s

- _{... 7} -s _•0 1.aa _-s.₇ _{-!. 4}

MAX. caMPRESSIONS, NONLJNEAR ANALYSJS MAX. CGMPRESSJONS, NONLINEAR ANALYSIS

Figure 5.10 (next 6 pages). Sequence of snapshots of arch AO and can- tilever CO from the nonlinear earthquake response of Pacoima Dam to the records of Figure 5.1 scaled by 2/3. Results are for the partially full reservoir: normal stresses (shaded, ten- sion positive, compression negative, amplitude given in MPa to one decimal place), joint openings (unshaded, amplitude given in cm to two decimal places), and deformed shape (solid line, original profile dashed line).

CM SCALE f~R

"if\'1

) \co 'i~'i

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91

CO~N

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r-1...JN

j~7

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- y

co

s ·a

z

x

.K].

.K]

[.KJ.

z

PP]

})-"~'\·"

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...

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