university of nigeriajosephat.c_1988_… · 2 . 0 2.1 2.2 title proposed strength grading nis-75...
TRANSCRIPT
University of Nigeria Research Publications
EZEOKONKWO, Josephat C.
Nam
e
PG/M.Eng./86/4150
Title
Uniaxial Compressive Strength of Sandcrete Hollow Blocks and its
Dependence on Geometry
Facu
lty
Engineering
Dep
artm
ent
Civil Engineering
Dat
e September, 1988
Sign
atur
e
UNIAXIAL COMPRE SANDCRETE HOLLOW BLO,s,, r u v u L r J uur ,IVU,IVLU
ON GEOMETRY
EZEOKONKWO JOSEPHAT CHUKWUGOZIE ( ~ G / ~ . ~ ~ G / 8 6 / 4 1 5 0 )
SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE O F THE MASTER OF
ENGINEERING I N CIVIL ENGINEERING
UNIVERSITY OF NIGERIA NSUKKA
C E R T I F I C A T I O N P A G E
T H I S P R O J E C T H A S B E E N A P P R O V E D F O R T H E D E P A R T M E N T O F C I V I L E N G I N E E R I N G
U N I V E R S I T Y O F N I G E R I A NSUKKA
----------------- EZE-UZOMAKA
AG. H E A D , DEPARTMENTOF C I V I L E N G I N E E R I N G
E X T E R N A L E X A M I N E R
------------------ DEAN P O S T - G R A D U A T E
S C H O O L
DEDICATION
Dedicated to my l a t e
bro ther , Mr. Donatus
Ezeokonkwo.
ABSTRACT
C o m p r e s s i v e s t r e n g t h o f a h o l l o w b l o c k h a s b e e n
c o n v e n t i o n a l l y c a l c u l a t e d o n t h e ba s i s o f t h e g r o s s area
of t h e a s - c a s t s u r f a c e of a h o l l o w b l c c k when t e s t e d i n
c o m p r e s s i o n . But it i s t h e s o l i d a r e a o f t h e b l o c k t h a t
a c t u a l l y t r a n s m i t s and s u s t a i n s t h e l o a d . The a s - c a s t
s u r f a c e s of h o l l o w b l o c k s l a c k smooth and p l a n e s u r f a c e s
r e q u i r e d f o r c o m p r e s s i o n tests. The i l l - e f f e c t s of uneven
s u r f a c e s must be overcome t h r o u g h t h e cumbersome p r o c e s s
of c a p p i n g , g r i n d i n g o r p a c k i n g w i t h a b e d d i n g m a t e r i a l .
But t h e s i d e s u r f a c e s of h o l l o w b l o c k s a r e p l a n e
and smooth and d o n o t r e q u i r e c a p p i n g and p o s s e s s good
p o t e n t i a l s for c o m p r e s s i o n tests. T h e r e f o r e , c o m p r e s s i o n
tests were d o n e o n t h e s i d e s u r f a c e s of hollow blocks and
. s t a t i s t i c g a l a n a l y s i s was used t o e s t a b l i s h t h e c o r r e l a t i o n
be tween t h e s t r e n g t h s measured o n t h e t w o p e r p e n d i c u l a r
S u r f a c e s .
C o m p r e s s i v e s t r e n g t h , we calculated on the basis of
t h e n e t areas and gross areas of the t w w p e r p e n d i c u l a r
s u r f a c e s . S t a t i s t i c a l var ia t ions i n compressive s t r e n g t h s
was i n v e s t i g a t e d , A l s o b y u s i n g c y l i n d e r mortar s t r e n g t h
w i t h a s p e c t r a t i o o f 2 , as t h e mean strength of t h e
p o p u l a t i o n f rom which t h e h o l l o w black s t r e n g t h s were
o b t a i n e d , we c a r r i e d o u t t-test analysis to d e t e r m i n e
iii
w h i c h of t h e c o m p r e s s i v e s t r e n g t h c a l c u l a t i o n i s b e t t e r .
B e c a u s e of t h e v a r i a b i l i t y i n h o l l o w volume and
c e n t r e - w e b to end-web r a t i o i n t h e h o l l o w b l o c k s u s e d
i n t h e m a s o n r y w a l l c o n s t r u c t i o n , t h e s t u d y i n v e s t i g a t e s
t h e effect of c e n t r e - w e b t o end-web r a t i o a n d h o l l o w
vo lume o n t h e c o m p r e s s i v e s t r e n g t h . W a t e r / c e m e n t a n d
Sand/Cement r a t ios are c o n s t a n t , C u r Zng and t e s t i n g
w e r e a c c o r d i n g t o t h e NIS-75 s p e c i f i c a t i o n f o r s a n d c r e t e
F o u r d i f f e r e n t 450x225x225mm h o l l o w b l o c k s t y p e s ,
e a c h w i t h end-webs o f 12.5 , 25 , 37.5, 50 and 60mm w e r e
s t u d i e d ,
From t h e s t u d y , i t was o b s e r v e d t h a t t h e s t a n d a r d
d e v i a t i o n a n d c o e f f i c i e n t o f V a r i a t i o n S t a n d a r d d e v i a t i o n
and c o e f f i c i e n t o f V a r i a t i o n is n o t c o n s t a n t f o r d i f f e r e n t
s t r e n g t h l e v e l s a n d a l s o t h e d i r e c t i o n o f l o a d i n g i n f l u e n -
ces t h e d i f f e r e n c e i n s t a n d a r d d e v i a t i o n and c o e f f i c i e n t
o f v a r i a t i o n s of t h e t w o p e r p e n d i c u l a r surface s t r e n g t h s .
A l s o , c o m p a r i s o n b e t w e e n the t w o p e r p e n d i c u l a r
s u r f a c e s t r e n g t h s showed a l i n e a r correlation w i t h d i f f e r e n t
s l o p e s for each s f the f o u r hollow block t y p e s . M u l t i p l e
c o r r e l a t i o n between t h e two susface s trengths a n d t h e
Centre-web to end-web ratio I s h i g h l y s i g n i f f c a n t t h a n t h e
l i n e a r c o r r e l a t i o n .
V a r i o u s c o m p r e s s i v e s t r e n g t h when compared w i t h
c y l i n d e r s t r e n g t h showed t h a t t h e n e t area ' s t r e n g t h
c a l c u l a t i o n is better t h a n t h e g r o s s area s t r e n g t h
c a l c u l a t i o n .
The e f f e c t o f c e n t r e - w e b to end-web r a t i o o n t h e
'Compressive s t r e n g t h i n d i c a t e s a p a r a b o l i c r e l a t i o n -
s h i p w i t h maximbin s t r e n g t h and t h e c o r r e s p o n d i n g C e n t r e -
web t o end-wcb ratio.
A l s o t h e h o l l o w volume affects t h e s t r e n g t h , t h e
s t r e n g t h dzcrzase:; yt-lornetrical' y w-i. t-.h irtcreasl.?~ .i.n khe
hol l -Y.J vo lumc .
ACKNOWLEDGEMENT
I w i s h to exp res s my s i n c e r e i n d e b t e d n e s s to my
S u p e r v i s o r , E n g r ( P r o f 1 0. J, Eze-Uzo maka , for h i s
v a l u a b l e c o n t r i b u t i o n s a n d g u i d a n c e d u r i n g t h e wo.rk.
I am g r a t e f u l to M r . S a b a s t i n e Osuchukwu a n d
M r . J o s e p h Asogwa b o t h of t h e C o n c r e t e L a b o r a t o r y ,
a n d M r . Erne NAukwe of t h e S t r u c t u r a l E n g i n e e r i n g
L a b o r a t o r y , U. N. N., for t h e h e l p g i v e n t o m e i n
c a s t i n g a n d t e s t i n g of t h e S p e c i m e n s .
My t h a . n k s t o M r . 0. 0. Oshiba, L i b r a r i a n N i g e r i a n
Road a n d B u i l d i n g R e s e a r c h I n s t i t u t e L a g o s , M r . B r i g h t
Nwokolo, .a P o s t g r a d u a t e s t u d e n t a t U n i v e r s i t y of B e n i n
a n d my f r i e n d s for t h e i r a s s i s t a n c e ,
I pm g r a t e f u l t o my b r o t h e r s Mr, P i u s Ezeokonkwo
a n d M r , S o l o m o n Gzeokonkwo far t h e i r moral a n d f i n a n c i a l
s u p p o r t ,
F i n a l l y , t o God be t h e G l o r y , f o r h i s g u i d a n c e
a n d i n s p i r a t i o n t h r o u g h o u t t h e work .
J o s e p h a t C. Ezeokonkwo
S e p t e m b e r ,1988
LIST OF FIGURES vi
F I G U R E TITLE PAGE
Mould d e t a i l s f o r d i f f e r e n t h o l l o w b l o c k s 23
Isotnetric view o f d i f f e r e n t h o l l o w b l o c k s 25
Grad ing c u r v e f o r s a n d used i n b l o c k s 27
C r o s s - s e c t i o n a l area o f side s u r f a c e of
a h o l l o w b l o c k . 30
R e l ~ t i o n betwwn s t r e n g t h s f tirid f xg 50
2'3 S i n g l e s l o p e r e l a t i o n b e t w e e n s t r e n g t h s
R e l a t i o n b e t w e e n s t r e n g t h s f and fz r , 55 *g
S i n g l e s lanc r e l a t i o n b e t w e e n s t r e n g t h s
s l o p e r e l a t i o n b e t w e e n s t r e n g t h s
f and f z n a 53 xg
2 ~ l . a tion b e t w e e n s t r e n g t h s f a n d f z n XI?
64
Single s l o p e r e l a t i o n be tween s t r e n g t h s
f a n d f 66 xn z n * P'ool e d s l o p e r e l a t i o n b e t w e e n s t r e n g t h s
Relz t i o n b e t w e e n maximum c r u s h i n g l o a d s
E f f e c t of c e n t r e - w e b t o end-web r a t i o o n c r u s h i n g loads, 8 2
E f f e c t of c e n t r e - w e b t o end-web r a t i o o n s t r e n g t h . 88
E f f e c t o f c e n t r e - w e b to end-web r a t i o o n s t r e n g t h fxn. 89
Effect of a v e r a g e s o l i d t h i c k n e s s o n s t r e n g t h
f z n * 94
v i i
4.5.0 E f f e c t of volume on c o m p r e s s i v e s t r e n g t h 100
4.5.1 E f f e c t of volume on c o m p r e s s i v e s t r e n g t h 102
E f f e c t o f volume on c o m p r e s s i v e s t r e n g t h
fxn '
v i i i L I S T CF TABLES
TABLE
2 . 0
2.1
2.2
T I T L E
P r o p o s e d s t r e n g t h g r a d i n g
NIS-75 minimum c o m p r e s s i v e s t r e n g t h
PAGE
C o m p r e s s i v e s t r e n g t h o f c o n c r e t e b l o c k s t y p e A a n d B 1 2
Deta i l s o f test R e s t u l t s 3 1
Mean c r u s h i n g l o a d , s t a n d a r d d e v i a t i o n and C o e f f i c i e n t o f Val : i a t ion . 34
Mean s t r e n g t h , s t a n d a r d d e v i a t i o n a n d c o e f f i c i e n t o f v a r i a t i o n f o r hand cotnpac t e d h o l l o w s a n d c r e t e b l o c k s . 3 5
t- test r e s u l t s 40
A s - c a s t s u r f a c e g r o s s A r e a s t r e n g t h a n d s i d e s u r f a c e g r o s s a r e a s t r e n g t h o f h o l l o w s a n d c r e t e b l o c k s . 4 9
A s - c a s t s u r f a c e n e t a r e a s t r e n g t h a n d side s u r f a c e g r o s s a r e a s t r e n g t h o f h o l l o w s a n d c r e t e blocks, . 5 4
As-cast n e t a r e a s t r e n g t h a n d s i d e s u r f a c e n e t a r e a s t r e n g t h o f h o l l o w s a n d c r e t e b l o c k s . 6 3
Maxi.mum c r u s h i n g l o a d s , Pz a n d Px , t h e i r r a t i o s and d i f f e r e n c e s . 76
P Values o f z /pCU, P ~ / P c u a n d U 81
f V a l u e s o f f z n / c u , f f f m / f c u , xg/ c y a n d U. 8 4
Plaxin~um ccntrc-web t o e n d web ratio c o r r e s p o n d - i.19 to the mapimum s t r e n q t h 89
f a n d Vo/Vs. 99 V a l u e s of f z n p f x g xn
Minimum c o r r e s p o
e s u r f ce ne a r e s tr 9 t h nd t n g h o l f o w vofurne $0 s o f d voPume ? ? O / ~ s ) 1 0 6
PLATE
L I S T OF PLATES
3 Hullow block types
4.3.1 Appearance of cracks as hollow block is tested on side surfaces.
4,3,2 Appearance of cracks as hollow b l o c k is tes ted as-cast,
PAGE
21
TABLE OF CONTENTS
DEDICATION . + e . o o
ABSTRACT ACKNOWLEDGEMENT LIST OF FIGURES LIST OF TABLES LIST OF PLATES LIST OF SYMBOLS
CHAPTER
1. INTRODUCTION ..a
1.1 Background to t h e P r o b l e m 1 .2 S t a t e m e n t of P r o b l e m 1 .3 O b j e c t i v e of S t u d y 2.4 S i g n i f i c a n c e o f S t u d y 1.5 S c o p e o f S t u d y
2 . LITERATURE REVIEW
3. TEST DETAILS ... 3.1 E x p e r i m e n t a l . Programme -. . 3 . 2 ' Mat ,er ia . l s . . . 3 . 3 F r e p a r a t i o n o f t e s t S p e c i m e n s .. .. 3.4 T e s t i n g . . .
4. RESULTS A N D DISCUSSION ... 4.1 C o n p u t a t i o n of S t r e n g t h . ..
4.2-0 S t a t i s t i c a l V a r i a t i o n i n C o m p r e s s i v e S t r e n g t h . . .
4 - 2 . 1 H o l l o w B l o c k S t r e n g t h V e r s u s C o n t r o l C y l i n d e r S t r e n g t h . . . .
4.3.0 C o m p a r i s o n o f As-cast S u r f a c e S t r e n g t h and side S u r f a c e S t r e n g t h of H o l l o w S a n d c r e t e B l o c k s . . . . . . .
4.4.0 E f f e c t o f Geometry ... . - . 4.5.0 E f f e c t of Volume . . . . r, .
Sa CONCLUSIONS A N D RECOMMENDATIONS 5.1 C o n c l u s i o n s . - . ... - . . 5.2 Recomrnenda t i o n s ... .-.
REFERENCES o o o - 0 . -
P a g e
i ii v
vi viii ix X
APPENDIXES 0 . . 0 , . . . .
1 INTRODUCTION
1.1 BACKGROUND TO THE PROBLEM
S a n d c r e t e h o l l o w b l o c k s a re the p r i n c i p a l m a s o n r y
u n i t s f o r b u i l d i n g c o n s t r u c t i o n i n N i g e r i a , I n Engi-
n e e r i n g f i e l d , t h i s m a t e r i a l is c o n s i d e r e d to be s imilar
to c o n c r e t e a n d is e x p e c t e d t o e x h i b i t p r o p e r t i e s s im i l a r
t o t h a t o f c o n c r e t e e x c e p t p e r h a p s for t h e l o w e r s t r e n g t h
of s a n d c r e t e .
C o n s i d e r i n g , t h e i m p o r t a n c e of s a n d c r e t e b l o c k s as 1
a major c o n s t r u c t i o n mater ia l i n N i g e r i a , NIS-75 s p e c i -
f i e d g u i d e l i n e f o r t h e p r o d u c t i o n of h i g h q u a l i t y b l o c k s
w i t h t h e desired s t r e n g t h g r a d i n g and o t h e r r e l e v a n t
p r o p s t i c s . F e d e r a l M i n i s t r y of Works d u r i n g Annua l
C o n f e r e n c e i n i(ano18 dec ided tc s p e c i f y 2.10P4/mm2 a s
t h e hi.nimum c o m p r e s s i v e s t r e n g t h f o r s a n d c r e t e b l o c k
for load G e a r i n g w a l l s o f 2 o r 3 s t o r e y b u i l d i n g .
The a b o v e minimum c o m p r e s s i v e s t r e n g t h s p e c i f i c a -
t i o n s f o r s a n d c r e t e b l o c k s were c a l c u l a t e d o n t h e b a s i s
o f t h e gross a r e a o f t h e a s - c a s t s u r f a c e o f s a n d c r e t e
b l o c k when tested i n c o m p r e s s i o n , T h i s means t h a t t h e
c o m p r e s s i v e l o a d c a r r y i n g c a p a c i t y i s e q u i v a l e n t for
s o l i d and ho1,low b l o c k s .
9 C u r t i n et al , S c h n e i d e r e t a l l o a n d Eze-Uzomaka
14
cr i t ic ized t h e above c o m p r e s s i v e s t r e n g t h c a l c u 1 . a t i o n
for h o l l o w blocks and uphe1.d t h a t t h e Compres s ive
s t r e n g t h s h o u l d he o n t h e b ~ s i s o f the net a r e a , s i n c e
i t i s t h e so l i d area of t h e b l o c k t h a t a c t u a l ly
9 t r a n s m i t s and s u s t a i n s t h e l o a d . C u r t i n e t a 1 o b s e r v e d
t h a t the compress . ive s t r e n g 21 of h o l l o w b l o c k c a n b e
ca lcu la ted o:~ the basis of t h e g r o s s a rea of the h o l l o w
b l o c k o n l y when h o l i o w b l o c k s a r e u sed i n c o n j u n c t i o n
w i t h g r o u t c o n c r e t e ,
Also t h e a s - c a s t surface area of h o l l o w s a n d c r e t e
b l o c k s or1 which t h e c.ompressive s t r e n g t h h a s b e e n
c o n v e n t i o n a l l y calculated, lacks sm5o th and p l a n e
surfaces required for compression tests. T h i s r e d u c e s
t h e Compressive strength s f h o l l o w b l o c k s t e s t e d a s - c a s t .
Before, a n y h c l l o w block i s t e s t e d as-cast, t h e i l l - e f f e c t s
of uneven surfaces must be overcome t h r o u g h t h e Cumber-
some p r o c e s s o f c a p p i n g , g r i n d i n g or p a c k i n g w i t h a
bedding m a t e r i a l .
But, the s i d e s u r f a c e s o f h o l l o w s a n d c r e t e b l o c k s
possess some potentials like ~1i10oth and p l a n e surfaces
r a q u i r e d f o r compressian t e s t s , The use of s i d e surface
f o r c q p r e s s i o n te:; ts w i l l remove t h e Cm9x.rsorne process
af c a p p i n g , grinding or p a c k i n g with a beddinq m a t e r i a l ,
i n order t o p roduce p l a n e and smooth s u r f a c e s ,
3
S u r v e y of block making i n d u s t r i e s i9394,596 revealed
t h a t t h e claim by ' var ious f a c t o r i e s t h a t t h e y p r o d u c e
the b e s t q u a l i t y blocks i s n o t t r u e as t h e s e blocks do
n o t meet t h e NIS-75 s p e c i f i c a t i o n for st.ccngth n o r the
Federal. M i n i s t r y of Work rninimcrn s t r eng ' ch s p e c i f i ca t i .on
f o r sandcrete b l o ~ k s . Also, they prodace ho l3 o w s a n d -
Crete b l c c k s w i t h different hallow volurnes ar?G centre-
web t o end-web r a t i o s . Vis i -a t i o n s i ! ~ h c ~ l ? ~ ~ vo lumes
and web thicknesses introduce d i s k i n c t i v e set o f va r i a -
tions i n t h e compressiv? s t z e n g t h , which n e e d e d to be
s t u d i e d .
1-2 STATEMZNT OF PROBLEM
H 0 . i iow scrtdcre t e block , h a v e S e e n convent ional ly
tested zs-cas t , and tile cornprcssive s t r e n g t h c a l c u l a t e d
o n t h e basis o f gross area, B u t , i t is the solid area
of the biock t h a t actual.1.y t r a n s m i t s and s u s t a i n s the
load.
A l s o , i t i s n o t c e r t a i n w h a t relationship e x i s t s
b e t w e e n compressive s t r c n g t h cbtalned by l o a d i n g on
two perpendicular surfaces of hollow black: as-cast
surface and side surface, The influence of block
geometry on t h e compressive s t r e n g t h of hollcw sar!d-
crete blocks needs to be i n v e s t i g a t e d .
T h e r e f o r e , this s t u d y investigates t h e u r i i a x i a l
compressive s t r e n g t h ~f h o l l o w s a n d c c e t e b210cks and
i t s dependence c;n cjeometry.
T h e broad aim of t h e study is to v a r y t h e hollow
volume, and the cen t re -web to end-web r a t io for t h e
different h o l l o w blocks. Compression tests were done
o n the . two p e r p e n d i c u l a r surfaces: as-cast s u r f a c e
and s i d e surface of hollow s a n d c r e t e blocks.
Then, C o m p r e s s i v e s t r e n g t h s were calculated o n
t h e b a s i s of g r o s s area and net area of t h e two per-
p e n d i c u l a r surf aces, i n order tu i n v e s t i g a t e :
S t a t i s t i c s ? variation i n C.ornpressive s t . r e r . g t h
of h o l l o w b l o c k s .
C o m p a r i s o n of s t r e n g t h s obtained by l o a d i n g a n
as-cas t s1.2rfaces and s ide surfaces 05 hollc-w b l o c k s .
Effect of Centre-web to end-web r a t i o cri thr?
Compressive s t r e n g t h of h o l l o w blocks,
Effect of I l o l l c ~ w volume o n the Compressive s t r e n g t h
of h o l l o w blocks.
1-4 S I G N I F I C A N C E OF S'TUDY
R e l a t i o n s h i p b e t w e e n strengths obkaineb b y l oad ing
on t h e two p e r p e n d i c u l a r surfaces: as-cast surface a n d
s i d e su r face , w i l l eliminate t h e cumbersome p rocess of
c a p p i n g , g r i n d i n g o r packing w i t h a bedding m a t e r i a l ,
rcq~frecl for t h e compression tes t o n a s - c a s t s u r f a c e s
of hollow blocks.
T h e e f fec t of centre-web to end-web ratio o n t h e
strengtr: i ~ i l ! 3e known, aild box such a f a c t o r c a n be
tised tc iniprove t h e cornpreszive s t r e n g t h of hollow
blocks. +
The general t . r end in the csmpressive strength w i l l
be known as t h e hohlew volume changes,
A sons t a n t snndfcement rat la of 6 and w a t e r / c e r n e n t
r a t i o of 0.7 were adopted for khe s t u d y . The 14-day
compression test which shaws 9 O p e r c e n t of 28-day
strength, and NIS-75 c u r i n g cor idi t ion w h i c h allows for
14-day test, w i t h 7 days waLer s p r i n k l i n g 24 hours after
the cas t ing o f the b l o c k is a d o p t e d throughout t h e s t u d y .
F o u r d i f f e r e n t hollow blocks type nure used i n t h e
s t u d y , Each has f i v e sets of hollo7d blocks w i t h v a r i a b l e
c e n t r e - w e b t o end-web ra t io* They are 30, 40.7, 50 and
60 p e r c e n t h o l l o w Slacks, and are ~hohr l in f i g . 3:i -2
In all, we have n i n e t e e n different hollow b!ocksl
The e x t e r n a l d i m e n s i o n s of t h e blocks are 450 x 225 x
225mm. T h e total number of b l o c k s used i n t h e study
i s 120 b l o c k s . 40.7H50 b l o c k was used as t h e control
w h i l e c a l c u l a t : i x j t h e h o l l o w dirner:sions o.F o t h e r b l o c k s ,
to e n s u r e u n i f o r m i t y i n t h e Ic?catj..~,?n of t h e c n v i k ies ,
2. LITERATURE REVIEW
NIS-75 defined h o l l o w sandcrete blocks as one i n
w h i c h one or mare l a r g e hole o r cavities pass through
t h e block and t h e s o l i d material i s between 5C% a n d
75% of t h e t o t a l volume of t h e block calculated from
"I the overall d;!rnensions. The code gave t h e m h i m u m
compressive s t r e n g kh requiremenk fcr hollow and solid
blccks. T h e load a t f a i l u r e d u r i n g t h e t e s t i s divided
by the gross area o f the hlocks. T h i s means t h a t t h e
compressive Load bearinq csapaci ty is equivalent f a r
s o i i d and hollow blocks,
T h i s spcc i r ' i ca t ion is in agreement with hollow
ccncretc block standard specifications 21,12,13 0
3u t t h e design cades 7 * 8 t 9 * for concre to masonry
u n i k s calculate t h e Coxpressive strength of hollow
blocks on t h e ba s i s of t h e n e t area cf the hollow
block.
~ e e - ~ z o r n a k a l ~ u p h e l d t h a t i t i s the solid area of
the block that xtuaily tfansmitr and sustains the
load. Conswpcntly? compressive strength of a h o l l o w
bl cck s h c u l d be aef inod w i t h respect to the s ~ l id area
o n l y ,
w h e r e P i s t h e failure l o a d , B is t h e overall. breadth
o f t h e test b l o c k , L i s the o v e r a l l length of t h e test
b l o c k , w h i l e a and b are t h e l e n g t h and L are t h e
Length and b r e a d t h r e s p e c t i v e l y of h o l l o w s I n the
as-cast f a c e .
The poor p e r f c r n a n c e o f h o l l o w s a n d c r e t e b l o c k s
both i n s t r u c t u r a l and n o n - s t r u c t u r a l w a l l s may n o t
be as a r e s u l t of poor workmanship b u t d u e to p e r h a p s
u n d e r design o r o v e r d e s i g n , This phenomenon may be
1 tracable to i n s u f f i c i e n t standard specif fca t fon fo r
h o l l o w aandcre te rijasonry units.
The oldest s p e c i f i c a t i o n f a r s a n d c r c t e b l o c k s
which was made i n the absence o f any s p e c i f i c a t i o n for
s a n d c r e t e blocks was proposed by ~ s i l i ~ ~ , which re-
commended t h a t for t w o o r t h r e e s t o r e y b u i l a i n g s 2
avssagc 28 days compressive s t r e n g t h of 2.07N/mm , and rnlini!r;un 28 d a y s ,compressive s t r e n g t h of 1.72N/mm
2
for i :?div i .dxt l blocks. T h i s s p e c i f i c a t i o n o n l y gave
the m i cimuin s t r e n g t h r-a t h e r t h a n minirnun! s t r e n g t h
g r a d i n g t h a t allows for the flexible d e s i g n of masonry
walls. It has a l i m i t e d application. ife&bel' polnted
15 o u t t h a t O s i l l i n h i s r ;pec l . f icaLior t ignored t h e m i s t u r e
movement a n d t h e r m a l v a r i a t i o n s c n t h e g r o u n d t h a t t h e
c r u s h i n g s t r e n g t h i s considered to he t h e m a i n f a c t o r
i n N i g e r i a .
S u r v e y 2,3,4,5,6 of b l o c k making i n d u s t r i e s i n
b o t h E a s t e r n and N o r t h e r n Nigeria h a v e shown t h a t t h e s e
s a n d c r e t e b l o c k s do not meet the NIS-75 or any o t h e r
s p e c i f : i c a t i o r r . V a r i a t i o n i n c o m p r e s s i v e s t r e r i g t h among - 1
factories is between 6% - 77.2%"",
Kopycinsk et a l l 7 o b s e r v e d t h a t t h e r 2 l a t i v e l y
h i g h c o n p r e s s i v e s t r e n g t h cf b l ~ c k i s r e q u i r e d b e c a u s e
of l o a d imposed o n the w a l l a n d d u r a b i l i t y of t h e b l o c k .
i n s e v e r e climdtic c o n d i t i o n ( h e a v y r a i n , l o w e x t e r n a l
a m b i e n t t e m p e r a t u r e , soaking and d r y walls). F l o r e k 4
o b s e r v e d that m o s t of t h e above mentioned h a r m f u l effect
do not o c c u r i n N i g e r i a , Specifically, h e r e are no
low e x t e r n a l t e m p e r a t u r e af fec t ing d u r a b i l i t y a n d s tabi-
l i t y of h o l l o w block structuresm
Taking i n t o a c c o u n t t h e a b o v e m e n t i o n e d a s p e c t s ,
the Federal M i n i s t r y of Works d u r i n g t h e Annua l C o n f e r e n c e
i n ~ a n o " d e c i d e d to lower requirements for s a n d c r e t e
b l o c k s as f o l l o w s : The 28-day c o m p r e s s i v e s t r e n g t h
( b a s e d o n g r o s s a r e a ) cf sandcrete block for load b e a r i n g
wal l s of 2 o r 3 s torey b u i l d i n g s h a l l riot be less t h a n
2 2.lN/mm , f o r an a v e r a g e of 6 b l o c k s , a n d t h a t t h e l o w e s t
s t r e n g t h of i n d i v i d u a i b l o c k s h o u l d n o t he less than
2 1 .75N/ rnm . T h i s s p e c i f i c a t i ~ n was adopted i n 1985.
The p r e s e n t s p e c i f i c a t i o n is n o t d i f f e r e n t fron
t h e s p e c i f i c a t i o n g i v e n by a s i l i , and does not al iow
for f l e x i b i l i t y i n d e s i g n of masonry wal.ls, And i t s
a p p l i c a t i o n is l i m i t e d to 2 o r 3 s t o r e y b u i l d i n g s ,
I 9 Onyemelukwe gave an o v e r v i e w of t h e D r a f t
s p e c i f i c a t : ~ o n Ecr t h e N I S - 7 5 spccif i c a t i o n for sand-
crete b l o c k Comp-cssive strength. H e point:ccl o u r t h a t
S t a n d a r d Crganization of N ige r i a e n v i s a g e d s p ~ c i f y i n g
t w o types of blocks, t y p e ' A 1 L c i n g load-bearing b l o c k s
and t y p e '9' non-load-bear in^. T h e l o a d - b e a r i n g b l o c k s
( type l A ' are s t r c n g th-graded while kype 'BF a 1 t h o u g h
n o t s t r - e n g t h - g r ~ d e d i s required to possess a minimum 2
c r u s h i n q s t r e n g t h of i.SN/inm . a
Tab12 2.0 P s o p o ~ e d S t r e n g t h Grading
A d d i t i o n a l g r a d e s advanc Designate 75% of designated i n g i n c r e m e n t of c treng t h e
NIS-75, like Bs2028 for c 0 n c r e . h b locks , s p e c i f i e d
t h r e e t y p e s s f blocks. T y p e ' A ' f o r lodd-bca . r ing and
n o n - l o a d - b e a r i n g external IJse; t y p e '8' f u r l o a d - b e a r i n g
internal use; o r for l o a d - b e a r i n g o r non-load-bea1-ing
e x t e r n a l use i f p r o t e c t e d by r e n d e r i n g o r other effect ive
m a n n e r ; t y p e 'c' f c r n o n - l o a d - b e a r i n g i n t e r n a l use, NIS-75
s p e c i f i e d rninhnurn s t rength r e q u i r e m e n t f o r the t h r e e t y p e s
of blocks as shown in t a b l e 2 , l below.
.. T a b l e 2 . 1 ' NIS--75 Minimum Compressive S t r e n g t h
Cc~npress i .ve S t r e n g t h
I-- ---- I I n d i v i d u a l -
Block Cla.s:sific:+ttfo~ Average of r3 blosks N/mm C 2 I Units ~ / r n r n % - i
The propos?d strength g f a d l n g is Setter t h a n NIS-75
because it cncdurages f l e x i b i l i t y i n d e s i g n . I t a l so
embraces any other specification f o r s a n a c r e t e i n c l c d i n g
NIS-75 for sandcrete blocks.
N I S - 7 5 specif i.cat:ion f o r s a n d c r e t e when compared
inlith BS2020 s t r e r r ~ t h grading f o r c o n c r e t e b lock of t y p e
' A 8 showed t h a t k h e minimum compressi.ve s t r e n ~ t h s p e c i f i e d
f o r s a n d c r e t e blocks of t y p e is g r e a t e r t h a n t h e minimum
s t r e n q k h - g r a d e for t y p e A c o n c r e t e blocks. T a b l e 2.2 shows
compressive strength of concrete blocks t y p e A and R.
Concrete blocks being a s t r o n q e r material. t h a n s andc re t c
b l o c k s h o v e minimum s t r e n g t h grade of 3.5~1'mrn~ l o r t y p e 3
A block:% w h i l e s a n d z r e L c has 7.5N/mrnL minimum compres-
sive s t r e n y t t ~ af Concr'zte b iocks type A and E,
TilLble 2r.Z . Corr%dE.SS 1x7s Str:.nyth 05 ar,crstc B l d a Type 11 and B -.
i n d i . v i d u a l #-I
I bl.ock s ( N/rnmL )
Typic a l S t r uc t . u r - a1 V n i t s
Clocks of I thcsc s t . r cng t h s
may n o t be readily a v a i l able,
cfypical S t r u c t u r a l . U n i t s
Thcr 2 is no ac?vant-age i n ;.: w i r l l 15s' partition
h a v i n g s t r e n g t h q rea t ly !n excess of t h c n::zdcd, and
t h e experience of t h e Cons t r i l c t i o n i n d u s t r y i n o u r
This m e t h o d a y p e a r s tc be s i m p l e s , and less e x p e n s i v e bu . t
demand the d e t e r m i n a t i o n of t h e t r u e characteristic w i a x j . a l
compressive ~ ; t r c n g t h of hollow blocks,
2,3,Bp2C,i1924 P a s t compress?.ori t e s t s cn safidcreke
compressive, r ? c r n U e r (e.9 rnffsonry walls) t h e situation is
s i m i l a r t o L t l ~ t e x i s t i n g in a t e s t block as-cmt . To t e s t
an t h e as-cast: s u r f a c e , c a p v i ~ l g or g r f n d i n g or- pack ing
w i t h a Sodding material j,s necessary in order t z p roduce
smooth and p lsnc surface.
FJf S-75 recwnmencecl capping mortar w i t h saarddcement
2 r a k b of uni ty anb $-day crus t ' i ing s t r e n g t h of 35.40N/rnm . 'l'his has k x e n Eoimd to inc rease t h e s t r e n g t h of bLock by
ii; shou?.d be noted t h d t tne two t e s t s measured the harciness
a n d d e n s i t y of t h e b l o c k r e s p e c t i v e l y .
The homogeneous n a t u r e o f t h e b l o c k s a l l o w s non-
d e s t r u c t i v e test o n a n y o f t h e t h r e e o r t h o g o n a l s u r f a c e s
to show l i t t l e v a r i a t i o n when t e s t e d u n d e r t h e same
c o n d i t i o n . B u t , i t d o e s n o t , t h e r e f o r e , h o l d t h a t
c o m p r e s s i o n test o n t h e t h r e e o r t h o g o n a l faces w i l l be
e q u a l .
I f p l a t e n f r i c t i o n o r e n d r e s t r a i n t c a n be e l i m i n a t e d
o r a t l e a s t r n i n i m i s e d , t h e n t h e u l t i m a t e c r u s h i n g s t r e n g t h
o f s a n d c r e t e b l o c k s s h o u l d be i n d e p e n d e n t o f t h e test
s p e c i m e n l e n g t h a s l o n g a s b u l k i n s i s a v o i d e d E 5 . S u c h
r e s u l t would i n d i c a t e , of c o u r s e , t h e t r u e u n i a x i a l
s t r e n g t h o f t h e s a n d c r e t e b l o c k . V a l u e s f o r t h e c h a r a c -
teris t ic c o m p r e s s i v e s t r e n g t h of walls c o n s t r u c t e d w i t h
blocks h a v i n g s h a p e f a c t o r s 0.6, 2.0 a n d 4.0 are g i v e n ,
9 i n d e s i g n c o d e . The p r o p a g a t i o n of ' c r a c k w i l l take p l a c e i n t h e p l a n e
p a r a l l e l to t h e d i r e c t i o n of c o m p r e s s i o n , n o t i n a p l a n e
c o n t a i n i n g t h e i n i t i a l c r a c k i n d u c e d b y s h r i n k a g e . I n
fac t , a l l c o m p r e s s i o n c r a c k i n g w i l l be p a r a l l e l to t h e 26
d i r e c t i o n o f c o m p r e s s i o n c o m p o n e n t n o r m a l to i t . I t i s t h e f a c e - s h e l l and t h e web t h a t c o n t r i b u t e
t h e a c t u a l s o l i d p a r t o f a n y h o l l o w b l o c k and a r e t h e
most s i g n i f i c a n t . T h e most o b v i o u s way i n w h i c h f a c e - s h e l l
and web t h i c k n e s s a f f e c t s t r e n g t h is t h a t d u r i n g compac t ion
u n d e r a g i v e n p r e s s u r e , t h e e f f e c t of f r i c t i o n a l r e s i s t a n c e
be tween t h e s i d e s o f t h e mould and t h e m a t e r i a l which
r e d u c e s t h e e f f e c t i v e n e s s of t h e c o m p a c t i o n and is more
pronounced when f a c e - s h e l l and web t h i c k n e s s e s a r e v e r y
small.
E z e - ~ z o m a k a ~ ' I found o u t t h a t t h e s o l i d p a r t s o f a
h o l l o w b l o c k a f f e c t s t h e 5 t r e n g t h of b l o c k s , t h e s t r e n g t h
i n c r e a s b s e x p o n e n t i a 11 y w i t h i n c r e a s e i n the a v e r a g e s o l i d
t h i c k n e s s of blocks. T h i s is described by the q u a t i o n :
where R is t h e r a t i o o f s t r e n g t h i n r e l a t i o n to sg
geomet ry effect and R t i s t h e ratio of t h i c k n e s s .
3 TEST DETAILS
3 .1 EXPERIMENTAL PROGRAMME
F a c t o r s s u c h as s a n d p a r t i c l e s i ze a n d g r a d i n g , a g e ,
b l o c k g e o m e t r y , c u r i n g c o n d i t i o n , w a t e r / c e m e n t r a t i o ,
s a n d / c e m e n t r a t i o , c a p p i n g , workmansh ip , tes t i n a t e c h -
n i q u e s , a n d r a t e o f l o a d i n g a re known t o e f f e c t t h e
s t r e n g t h o f s a n d c r e t e b l o c k s . Each v a r i a b l e r e s t i n g
upon i t s e f f e c t , i n t r o d u c e s , i t s own d i s t i n c t i v e set
o f v a r i a t i o n o n t h e s t r e n g t h . A l l t h e s e v a r i a t i o n
n e e d e d t o be s t u d i e d .
I n v e s t i g a t i o n i n t o t h e e f f e c t o f s a n d / c e m e n t
r a t i o , w a t e r / c e m e n t r a t i o , s ,and p a r t i c l e s i ze a n d
g r a d i n g , a g e , c u r i n g c o n d i t i o n , b l o c k g e o m e t r y a n d
c a p p i n g o n t h e s t r e n g t h o f h o l l o w s a n d c r e t e b l o c k s
h a v e b e e n u n d e r t a k e n ( 2 , 5 , 2 0 , 2 4 , 2 7 , 2 8 ) w hi^ s t u d y
w h i c h i n v e s t i g a t e s t h e u n i a x i a l c o m p r e s s i v e s t r e n g t h
o f h o l l o w s a n d c r e t e b l o c k s a n d i t s d e p e n d e n c e o n geo-
m e t r y , i s p r i m a r i l y aim a t t h e f o l l o w i n g :
a ) t h e s t a t i s t i c a l v a r i a t i o n i n s t r e n g t h o f h o l l o w
s a n d c r e t e b l o c k s .
b ) C o m p a r i s o n o f s t r e n g t h s o b t a i n e d b y l o a d i n g o n
a s - c a s t s u r f a c e a n d s i d e s u r f a c e o f h o l l o w b l o c k s .
( c ) e f f e c t o f c e n t r e - w e b t o end-web r a t i o o n t h e
s t r e n g t h o f h o l l o w b l o c k s ; a n d
d ) e f f e c t of h o l l o w v o l u m e o n t h e s t r e n g t h o f h o l l o w
b l o c k s *
To c a r r y o u t t h e abovi s t u d y , some f a c t o r s which
a f f e c t s t r e n g t h are c o n s i d e r e d c o n s t a n t , w h i l e o t h e r s
are t a k e n to be v a r y i n g . T h o s e f a c t o r s c o n s i d e r e d to
be c o n s t a n t i n c l u d e :
S a n d / c e m e n t r a t i o , w a t e r / c e r n e n t r a t i o , c u r i n g c o n d i t i o n ,
a g e , , s a n d p a r t i c l e s i z e and g r a d i n g a n d r a t e o f l o a d i n g .
S t u d y 2 9 5 7 2 0 , 2 4 h a v e shown t h a t a s s a n d / c e m e n t
r a t i o i n c r e a s e s , s t r e n g t h d e c r e a s e s . The i n v e r s e v a r ia-
t i o n of t h e s t r e n g t h w i t h s a n d / c e m e n t r a t i o is a s a
r e s u l t o f i n c r e a s e i n t h e s a n d c o n t e n t , which p r e s e n t s
g r e a t e r s u r f a c e making i t i m p o s s i b l e f o r t h e c e m e n t p a s t e
to h a v e e f f e c t i v e i n t e r a c t i o n n e c e s s a r y f o r b o n d i n g , and
f u l l s t r e n g t h d e v e l o p m e n t , A c o n s t a n t s a n d / c e m e n t r a t i o
o f 6 is u s e d t h r o u g h o u t t h e programme, u n l e s s o t h e r w i s e
s t . a t e d .
The v a r i a t i o n of s t r e n g t h w i t h w a t e r / c e n e n t r a t i o
h a s b e e n i n v e s t i g a t e d 2'15720*24. I t was o b s e r v e d t h a t
as w a t e r / a e m e n t r a t i o i n c r e a s e s f o r a n y p a r t i c u l a r s a n d /
c e m e n t r a t i o , t h e s t r e n g t h i n c r e a s e s up to a peak beyond
w h i c h t h e s t r e n g t h w i l l s t a r t t o d e c r e a s e , The water/
c e m e n t r e t i o u sed i n t h e programme is 0.7. T h i s i s t h e
w a t e r / c e r n e n t r a t i o t h a t would g i v e t h e n e c e s s a r y h y d r a -
t i o n r e q u i r e d f o r S t r e ~ q t h d e v e l o p m e n t , f o r t h e p a r t i c u -
l a r s a n d / c e r n e n t r a t i o u s e d . T h e r e f o r e , w a t e r / c e m e n t
r a t i o o f 0.7 would be a d o p t e d t h r o u g h o u t t h e programme,
u n l e s s o t h e r w i s e s t a t e d . See A p p e n d i x A ,
C u r i n g c o n d i t i o n is a n o t h e r f a c t o r t h a t affects
t h e s t r e n g t h d e v e l o p m e n t o f s a n d c r e t e b l o c k s . B l o c k s
c u r e d , u n d e r d i f f e r e n t c u r i n g c o n d i t i o n s h a v e b e e n f o u n d
t o h a v e d i . f f e r e n t s t r e n g t h s 2 , 1 4 , 2 0 , 2 4 , 2 7
Water s p r i n k l i n g o n b l o c k s a n d o p e n s h a d e c u r i n g
is common among t h e local b l o c k m a k i n g i n d u s t r i e s ,
S t r e n g t h o f b l o c k s which a re c u r e d w i t h w a t e r s p r i n k l e d
o n them i s h i g h e r t h a n t h e s t r e n g t h s of b l o c k s c u r e d
w i t h o u t water s p r i n k l i n g ,
T h e e f f e c t o f w a t e r s p r i n k l i n g i s to augment t h e
w a t e r I n t h e mix which i s r e q u i r e d f o r h y d r a t i o n , a n d
h e n c e t h e e f f e c t o f w a t e r s p r i n k l i n g becomes more p r o -
nounced a t low w a t e r / c e m e n t r a t i o s , Beyond t h e optimum
w a t e r / c e m e n t r a t i o , c u r i n g w i t h water s p r i n k l i n g s h o u l d
be d e t r i m e n t a l to s t r e n g t h d e v e l o p m e n t , T h i s may c r e a t e
v o i d s as a r e s u l t o f w a t e r w i t h d r a w a l f rom t h e b l o c k a n d
d o e s n o t p e r m i t p r o p e r b o n d i n g ,
I t s h o u l d be n o t e d , t h a t r e l a t i v e h u m i d i t y a n d
t e m p e r a t u r e a r e n o t augmented i n t h e v a r i a b l e c o n s t a n t s
b u t are t a k e n to be u n i f o r m t h r ~ u g h o u t t h e d u r a t i o n of
t h e programme, T h e 14-day test w h i c h shows 90% of t h e
28-day s t r e n g t h a n d t h e NIS-75 c u r i n g c o n d i t i o n which
a l l o w s f o r 14-day tes t , w i t h 7 d a y s w a t e r s p r i n k l i n g
2 4 h o u r s a f t e r t h e c a s t i n g o f t h e s a n d c r e t e b l o c k s i s
a d o p t e d t h r o u g h o u t t h e e x p e r i m e n t ,
To a c h i e v e t h e o b j e c t i v e of t h e s t u d y , t h e f o l l o w i n g
v a r i a b l e s were i n t r o d u c e d in t h e g e o m e t r y o f t h e b l o c k :
t h e h o l l o w s i z e a n d l o c a t i o n of h o l l o w ( c a v i t y ) . F o u r
d i f f e r e n t 45Ox225x225rnm h o l l o w b l o c k t y p e s w e r e u s e d
i n t h e programme. T h e i r p e r c e n t a g e h o l l o w area i s
based o n t h e a s - c a s t surface area.
T h e s e i n c l u d e 30%, 40.7%, 50% and 60% h o l l o w s a n d -
crete b l o c k s . F i g 3.1.1 and 3.1-2 shows t h e d i f f e r e n t
b l o c k g e o m e t r y , t h e d i m e n s i o n s o f t h e h o l l o w , a n d t h e
l o c a t i o n s o f t h e h o l l o w , . A l l t h e s a n d c r e t e b l o c k s
h a v e cores o r h o l l o w s w i t h a p p r o x i m a t e l y p a r a l l e l s i d e s ,
w i t h o n l y a m i n i m a l relief a n g l e ,
Each h o l l o w b l o c k g r o u p e,g 30% h o l l o w b l o c k s h a v e
end-web, t h i c k n e s s a s 12.5, 25 , 37,5, 50 , and 60 rnm and
are r e p r e s e n t e d as 30H12.5, 30H25, 30H37.5, 30H50 and
30H60, T h e o b j e c t i v e of end-web v a r i a t i o n is to find o u t
t h e p o s s i b l e c e n t r e - w e b t o end-web r a t i o t h a t w i l l give
FIG 3-34 MOULD DETAILS FOR 30H12 J130H60AND 40 7Hl2 5 - 40 7 H6O HOLLOW BLOCKS
. ~ - -- - r-- -<-. '
? 30H37-5 40-7H37.5 SOH376
; I @.fl.@.@# I 30H50 I- , WH45 -
FIE 3.1.2 I SOME TRIG VIEW OF , / DIFFERENT ,
, HOLLOW BLOC
, 30H60 : 40.7H60 1 50 H60
3,2 MATERIAL
T h e sand u s e d i n t h e programme was o b t a i n e d from
O p i R i v e r i n Nstikka Local. Government Area of Anambra S t a t e .
F ig 3.2.0 shows t h e ~ r w ! i n ~ c u r v e f o r i)?i s a n d L I S ~ ? ~ i n
making t h e b l o c k s . I t is t h e major s o u r c e of s a n d f o r t h e
b l o c k making i n d u s t r i e s i n t h e l o c a l governmmt. h s u r v e y 5
of b l o c k i n d u s t r i e s i c 1 t h e tw:) Eastern S t a t e s (Imo a n d
Anambra S t a t e s ) , O p i R i v e r s a n d was r a t e d 1 2 t h p o s i t i o n o u t
o f 1 3 s o u r c e s o f sand u s e d by t h e f a c t o r i e s v i s i t e d . T h i s
i s d u e to i t s h i g h s p e c i f i c s u r f a c e v a l u e .
T h e ' c e m e n k was o r d i n a r y p o r t l a n d c e m e n t ( B e n u e
Cement Company, R.C,C.) f r o m Gboko i n Benue S t a t e o f
a N i g e r i a , This was u s e d b e c a u s e o f i t s a v a i l a b i l i t y . The
c o r n p o s i . t i o n and p r o p e r t i e s o f t h e c e m e n t c o m p l y w i t h
N I S 11: 1974,
Tap wate r was u s e d f o r a l l m i x e s .
3 .3 PREPARATION OF TEST SPECIMENS
T h e mixing was m a n u a l l y d o n e , Wooden b l o c k moulds
w e r e c o n s t r u c t e d a c c o r d i n g t o t h e size o f h o l l o w blocks
u s e d i n t h e programme, C o m p a c t i o n was d o n e i n t h r e e l a y e r s ,
FIG '3-2-C
28
e a c h tamped 35 times w i t h t h e tamping .wooden r o d .
A f t e r c a s t i n g , t h e b l o c k s were demoulded and l e f t
i n t h e L a b o r a t o r y f o r 24 h o u r s . C u r i n g s t a r t s 24 h o u r s
a f t e r c a s t i n g by water s p r i n k l i n g o n c e a d a y f o r 7 d a y s
and t h e n left to m a t u r e f o r a n o t h e r 7 d a y s i n s i d e t h e
L a b o r a t o r y i n a c c o r d a n c e w i t h NIS-75 s p e c i f i c a t i o n f o r
c u r i n g .
T h e p r o c e d u r e o f r u b b i n g down t h e test f a c e s w i t h
Carborupdum s t o n e was u sed to achieve t h e d e s i r e d e v e n
s u r f a c e f a r a s - c a s t s u r f a c e s .
T h e w e i g h t o f t h e b l o c k s , c u b e s and c y l i n d e r
s p e c i m e n s were f i r s t d e t e r m i n e d f r a n which t h e d e n s i t i e s
are computed.
*Each b l o c k was c r u s h e d i n a 2000KN c a p a c i t y Denison
machine. The Load was a p p l i e d to t h e b l o c k t h r o u g h a
457mm x 254mm x 25mm steel p l a t e p l a c e d o n top o f t h e
block. Both t h e s teel p l a t e andl t h e p l a t e n bavb smooth ,
machined faces, b u t o t h e r w i s e no e f f o r t was made t o p r o d u c e
f r i c t i o n l e s s e n d s .
4.0 RESULTS AND DISCUSSION
4.1 COMPUTATION OF STRENGTH
C o m p r e s s i v e s t r e n g t h of a h o l l o w b l o c k h a s b e e n
c o n v e n t i o n a l l y c a l c u l a t e d o n t h e b a s i s o f t h e g r o s s area
o f t h e a s - c a s t s u r f a c e o f a h o l l o w b l o c k when t e s t e d i n
c o m p r e s s i o n . C u r t i n e t a l S c h n e i d e r e t a1 ( 1 0 ) a nd
Eze-Uzomaka (14) c r i t i c i z e d the a b o v e c o m p r e s s i v e s t r e n g t h
c a l c u l a t i o n f o r h o l l o w b l o c k s a n d ' u p h e l d t h a t t h e compres -
s i v e s t r e n g t h s h o u l d be o n t h e bas i s o f t h e n e t area, s i n c e
i t is t h e s o l i d a r e a o f t h e b l o c k t h a t a c t u a l l y t r a n s m i t t s
a n d s u s t a i n s t h e Load. C u r t i n e t a1 o b s e r v e d t h a t t h e
c o m p r e s s i v e s t r e n g t h of h o l l o w b l o c k s c a n be c a l c u l a t e d o n
t h e b a s i s o f t h e g r a s s area o f - t h e h o l l o w b l o c k o n l y when
h o l l o w b l o c k s a r e u s e d i n c o n j u n c t i o n w i t h g r o u t c o n c r e t e .
' ~ o m ~ r e s s i v e s t r e n g t h s were c a l c u l a t e d o n t h e b a s i s o f
t h e n e t areas and g r o s s areas of t h e t w o p e r p e n d i c u l a r
s u r f a c e s , T h e s t r e n g t h o f h o l l o w b l o c k s t e s t e d as-cast
were c a l c u l a t e d as:
w h e r e f is t h e g r o s s area s t r e n g t h of b l o c k t e s t e d KJ
as-cast; PZ i s t h e as-cast c r u s h i n g l o a d ; L i s t h e o v e r a l l
l e n g t h o f b l o c k a n d B i s t h e w i d t h o f t h e b l o c k a n d
- P f z n
-------(4,1,1) .&b,
w h e r e f z n is the n e t area s t r e n g t h of b l o c k t e s t e d a s - c a s t ;
a a n d b a re l e n g t h and w i d t h of ho l low.
T h e c o m p r e s s i v e s t r e n g t h o f s i d e s u r f a c e t e s t e d
h o l l o w b l o c k s were c a l c u l a t e d on t h e basis of:
where f is t h e g r o s s area s t r e n g t h o f s i d e s u r f a c e tested x9
b l o c k s a n d Px i s t h e s i d e s u r f a c e c r u s h i n g l o a d
w h e r e f x n i s t h e n e t area s t r e n g t h o f s i d e s u r f a c e tested
b l o c k s a n d An is t h e area of t h e s h a d e d cross web p o r t i o n s
shown i n f i g 4.1.0.
Fig 4.1.0 C r o s s - s e c . t i o n a 1 Area of s i d e s u r f a c e of a h o l l o w b l o c k ,
w h e r e An = H ( 2 t e + tc)
a n d H is t h e h e i g h t of t h e b l o c k .
tc i s Cent re -web t h i c k n e s s .
te i s t h e end-web t h i c k n e s s .
The r e s u l t s are Summarised below i n t ab le 4.1.0
Type of
Blocks
I
' 30H12.5
' 30Fi12.5,
1301125 '
30II25
3OH37e5
; 30H37.5
30H50 . ..
I 30H50
30H60
30H60
40 7H12eE
\4~.71.112,5
1 Detail
Surf ace Tcstd
of T e s t R e s u l t
Ratios
3.09
1-82
1-82
1-18
1.18
10.00
10 moo
N e t
Surf ace Ratios Tes t ed I --
N e t
50 .a0 33.750
60 -00 33,750
60.00 33.750
SO. 00 33.750
50,63 27.000
50.63 27.000
50.63 27.000
50.63 270000
50.63 27.OCO
40.50 20.250
20.50 20.250
10850 ?O. 2'30
20.50 !O.25O
~ e v i l l e ~ ' p o i n t e d o u t t h a t b o t h s t a n d a r d d e v i a t i o n
a n d mean s t r e n g t h i n c r e a s e w i t h a decrease i n t h e s i z e
of t h e s p e c i m e n , so t h a t fo r t h e v e r y small s i z e i t i s t o
be e x p e c t e d t h a t t h e s p r e a d i n t h e i n c r e a s e d s t r e n g t h , a s
i n d i c a t e d by t h e s t a n d a r d d e v i a t i o n w i l l be r a t h e r h i g h .
It was a l s o f o u n d t h a t t h e c o e f f i c i e n t o f variation
decrease as tl;e s p e c i m e n s i z e i n c r e a s e s 3 ' , a l l w i t h
r e f e r e n c e t o concrete,
For c o n c r e t e , e x a n i n a t i o n of p r e v i o u s i n v e s t i g a t i o n s
i n d i c a t e t h a t t h e s t a n d a r d d e v i a t i o n a n d c o e f f i c i e n t o f
v a r i s t i o n a r c n o t c o n s t a n t f o r d i f f e r e n t s t r e n g t 5 l e v e l s ,
Gn t h e bas i s of t h e a v a i l a b l e test d a t a 2 2 , 3 1 , 3 2 , 3 3 , 3 4 i t
a p p e a r s t h a t t h e a v e r a g e c o e f f i c i e n t of v a r i a t i o n c a n be
t a k e n c o n s t a n t a t l o % , 15X, a n d 20% f o r s t r e n g t h l e v e l s
b e l o w 27.6 bJ/mm2 ( 4 0 0 U p s i ) to r e x c e l l e n t , a v e r a g e a n a p o o r
c o n t r o l r e s p e c t i v e l y . F o r c o n c r e t e w i t h a n a v e r a g e s t r e n g t h
2 a b o v e 27.6N/mm t h e s t a n d a r d d e v i a t i o n r e m a i n s a p p r o x i m a t e l y
2 c o n s t a n t w i t h v a l u e s of 2.76N/rnm , 4.14~/mm' a n d 5.52N/mm
2
for t h e t h r e e levels of c o n t r o l l i s t e d a b o v e .
T h e aim or a n y h o l l o w b l o c k m a k i n g i n d u s t r y i s t o p r o d u c e
a h o l l o w s a n d c r e t e h l o c k s w h o s e s t r e n g t h meets t n e "minimum
s t r e n g t h " s p e c i f i e d i n tne coaes I n o r d e r t o make a
g o o d j u d g e m e n t a b o u t t h e q u a l i t y of s a n d c r e t e b l o c k s p r o d u c e d ,
t h e m a n u f a c t u r e r m u s t know v a r i a t i o n i n t h e c o m p r e s s i v e
s t r e n g t h o f b l o c k s .
T h i s c a l l s t o r t n e d e t e r m i n a t i o n of t h e mean s t r e n g t h ,
s t a n d a r d d e v i a t i o n a n d c o e f f i c i e n t o f v a r i a t i o n o f t h e t e s t e d
s a m p l e . I t e n c o u r a g e s p e r i o d i c a l t e s t i n g of blocks b y t h e
m a n u f a c t u r e r s to e v a l u a t e t h e q u a l i t y o f t h e i r b l o c k s .
I n t h i s s t u d y , e a c h h o l l o w b l o c k g r o u p h a s less t h a n
t . h i r t y s a m p l e s . Tab le 4.2.0 g i v e s t h e d i s p e r s i o n Coef f i-
c i e n t s f o r t h e maximum C r u s h i n g l o a d s o n t h e two p e r p e n d i c u l a r
s u r f aces,
T a b l e 4.2.0 Mean C r u s h i n g Load , S t a n d a r d Deviation a n d C o e f f i c i e n t o f V a r i a t i o n :
P'IEAN STA 1\!DARD COE FF IC TE ItT OF TYPE CRUSti ING LOAD DEVTATTCN VAR TATION ( X )
S t a t i s t i c a l variation i n c r u s h i n g l o a d shows t h a t t h e
mean c r u s h i n g l o a d s f o r t h e t w o p e r p e n d i c u l a r s u r f a c e s h a v e
t h e same t r e n d . T h e n e a n C r u s h i n g l o a d i n c r e a s e s a s t.he
h o l l o w v o l u m e decreases. S t a n d a r d d e v i a t i o n a n d C o e f f i c i e n t
of v a r i a t i o n showed i r r e g u l a r t r e n d , T h e c o e f f i c i e n t of
v a r i a t i o n r a n g e s from 4.95%-13.195% and 11.612%-19,320%
r e s p e c t . i v e l y f o r t h e as-cast s u r f a c e and s i d e surface
r u s h i n g l o a d s - The s t a n d a r d d e v i a t i o n r a n g i n g from
13.236KN-41,380KN and 18,423KN-30.855KN w e r e achieved
for a s - c a s t s u r f a c e and s i d e s u r f a c e of hand c o m p a c t e d
h o l l o w b l o c k s ,
I n t a b l e 4.2,1 is shown t h e d i s p e r s i o n c o e f f i c i e n t
f o r t h e s t r e n g t h o f h o l l o w s a n d c r e t e b l o c k s , I t c a n b e
., s e e n t h a t , t h e mean s t r r 2 n g t h d e c r e a s e s w i t h i n c r e a s e i n
h o l l o w vo lume, except f o r t h e n e t area s t r e n g t h o f t h e
s i d e s u r f a c e s , w h e r e t h e b l o c k g roup 60H12.5-60H45 showed
g r e a t e r mean s t r e n g t h o v e r b l o c k g r o u p s :
50H12.5-50F160 a n d 40.7Hl2.5-fiOH60, T h i s s u p p o r t s . .
T ~ b l e 4.2,1 Mean S t r e n y t h , S t a n d a r d d e v i a t i o n ar:d Cocf f i . c i e n t
-- of -____T__ V a r k a t i o n f o r Hand Compacted H o l l o w Sandcrete B l o c k s , -- Standard ,deviation Coefficient of
Area Area A r e a Area
t h e o b s e r v a t i o n t h a t t h e s t r e n g t h of t h e s m a l l s p e c i m e n s
3 1 is o n t h e a v e r a g e l a r g e r t h a n t h a t of t h e l a r g e r s p e c i m e n s . The C o e f f i c i e n t of v a r i a t i o n h a s n o d e f i n e d t r e n d , b u t a
v a l u e of 4,95%-11.924% a n d 11,612%-19. 32% w e r e a c h i e v e d
f o r hand-compac ted h o l l o w b l o c k s t e s t e d o n two p e r p e n d i c u -
l a r s u r f a c e s ,
The s t a n d a r d d e v i a t i o n h a s i r r e g u l a r t r e n d f o r a s - c a s t
s u r f a c e s t r e n g t h and v a r i e s f r o m 0 . ~ 2 1 ~ / m r n ~ - 0 . 3 9 5 ~ / m m ~ and
2 ., 0 ~ 1 3 1 ~ / m r n ~ ~ 0 ~ 4 1 0 ~ / m r n f o r as-cast s u r f a c e n e t area a n d
g r o s s area s t r e n g t h s r e s p e c t i v e l y . The side s u r f a c e
s t a n d a r d d e v i a t i o n f o r t h e n e t area s t r e n g t h shows i r r e g u l a r
t r e n d a n d r a n g e s f r o m 0 .697~/mm~-1.124~/ rnrn~. T h e s i d e
s u r f a c e g r o s s a r e a s t r e n g t h h a s s t a n d a r d d e v i a t i o n t h a t
s h o w s t h e same t r e n d a s h o l l o w vo lume i n c r e a s e s w i t h
2 s t a n d a r d d e v i a t i o n o f 0 . 1 8 4 ~ / m m ~ - 0 . 3 0 6 ~ / m m .
The m a j o r s o u r c e s o f v a r i a t i o n s i n s a n d c r e t e h o l . 1 0 ~
b l o c k s s t r e n g t h a r e t h e v a r i a t i o n s i n m i x i n g , c a s t i n g , a n d
c u r i n g m e t h o d s and t h e v a r i a t i o n s i n t e s t i n g p r o c e d u r e s .
The v a r i a b i l i t y o f s a n d c r e t e b l o c k s t r e n g t h d e p e n d s o n
t h e q u a l i t y c o n t r o l of t h e m a n u f a c t u r i n g o p e r a t i o n s .
F o r s a n d c r e t e b l o c k s , a n e x a m i n a t i o n o f p r e v i o u s
i n v e s t i g a t i o n s i n d i c a t e s t h a t t h e s t a n d a r d d e v i a t i o n a n d
t h e C o e f f i c i e n t of v a r i a t i o n are n o t c o n s t a n t f o r d i f f e r e n t
s t r e n g t h T h i s s t u d y c o n f i r m s t h i s o b s e r v a t i o n
a n d a l s o t h a t t h e d i f f e r e n c e i n t h e d i r e c t i o n o f l o a d i n g
i n f l u e n c e s t h e d i f f e r e n c e i n t h e s t a n d a r d d e v i a t i o n a n d
c o e f f i c i e n t o f v a r i a t i o n s of t h e two p e r p e n d i c u l a r s u r f a c e
s t r e n g t h s ,
T h e as-cast s u r f a c e n e t area s t r e n g t h h a s mean
s t r e n g t h of 4 . 3 2 5 ~ / m m ~ and s t a n d a r o d e v i a t i o n of 0.578N/mrn 2
w i t h a c o e f f i c i e n t o f v a r i a t i o n of 13-44?>, T h e g r c s s area
2 . , s t r e n g t h ha's mean v a l u e cf 2,447N/mm , s t a n d a r d deviation
S i d e s u r f a c e t:?sted b l o c k s , h a v e n e t a rea mean s t r e n g t h as
2 b.341N/mm , s t a n d a r d d e v i a t i o n a s 1.093~/mm' a n d c o e f f i c i e n t
of v a r i a t i ~ n ds 23-46:',. For t h e g r o s s a rea , mean s t r e n g t h
2 2 i s 1.701N/rn1n , s t h n d a r d d e v i a t i o n i s 0,679N/rnrn a n d co-
T h e C o e f f i c i - e n t o f v a r i a t i o n a s a measure of t h e
u n i f o r m i t y of h o l l o w s a n d c r c t e b l o c k p r o d u c t i o n , is of t e n
u s e d t o c h a r a c t e r i s e t .he q u a l i t y o f p r o d u c t i o n . T h e l o w e r
t h e C o e f t i c i e n t cf v a r i a t i o n , t h e more u n i f o r m is t h e
c o n c r e t e p r o c l u c t l o n a n a t h e B e t t e r t h e q u a . t i t y of a
36 p r o d u c t i o n . C o m p r e s s L o n tcsts on t h e t w o p e r p e n d i c u l a r s u r f a c e s ,
showed t h a t r i B t area s t x e n g t h h a s laxer' C u c t t i c i c n ! : of
v a r i a t i o n t h a n g r o s s a rea s t r e n g t h , a n d t h e r e f o r e , a
better q u a l i t y .
4.2.1 HOLL,OW BLOCK STRENGTH V E R S U S CON'I'ROL CYLINL)EK S'I'KENG'I'H
l ' h e C o n t r o l c y l i n d e r s t r e n g t h is ~ . 0 9 3 ~ / m r n ~ w i t h
2 s t a n d a r d d e v i a t i o n o f 0.821N/mm a n d C o e f f i c i e n t of v a r i a -
t i o n of 16.124% from t h e s i x t e s t s a m p l e s . T h e s t r e n g t h
of h o l l o w ~ b l o c k c a n be g r e a t e r or less t h a n C y l i n d e r
s t r e n g t h of t h e same s a n d c r e t e mix . T h i s d i f f e r e n c e is
d u e t o t h e e f f e c t s of t h e g e o m e t r y , v o l u m e of h o l l o w ,
t h e d i r e c t i o n of l o a d i n g a n d t h e b e a r i n g s u r f a c e area o f
t h e h o l l o w b l o c k u s e a t o c o m p u t e t h e s t r e n g t h .
T h e r a t l o oi- h o l l o w block s t r e n g t h t o t h e c y l i n d e r
s t r e n g t h i s a c o n s t a n t f o r e a c h b l o c k g e o m e t r y , b u t n o
u n i v e r s a l c o n s t a n t v a l u e e x i s t . F o r h o l l o w b l o c k s tested
as-cast, t h e n e t area s t r e n g t h t o c y l i n d e r s t r e n g t h r a t i o
v a r i e s f r c m 0.698-1.030, a n d t h e g r o s s area s t r e n g t h t o
C y l i n d e r s t r e n g t h r a t i o v a r i e s t r o m O.28U-U.72I.
P'or side s u r f a c e t e s t e d b l o c k s , . t h e n e t a rea s t r e n g t h
to C y l i n d e r s t r e n g t h r a t i o v a r i e s from U.705-1.36b w h i l e
t h e g r o s s area s t r e n g t h t o C y l i n d e r s t r e n g t h r a n g e s trom
U. %bl-0.580.
I n t h i s work, ccinpressiVC s t r e n y t h s were calculatca
o n t h e b a s i s o? net: a r e a and g r o s s area, .LC, s t i l l r e r n a i n s
to f i n d o u t w h i c h ci2e sctually r e p r e s e n t t h ? Compressive
s t r e n g t h o f t h e olock, if w e take the cylinoer s t r e n g t h t o
be t h e rrlcan c c m p r e s s i v e s k r e n g ' l h of t n e p o p u l r t i . o n . I n
o r d e r word, hr'ly hollaw block g r o u p mean s t r e n g t h (E) 1 s
ar, estimate of t.he true p o p u l ~ i t i o n mean ~ h i c h is t h e
cy l rzc ie r s t r e n g t h . The h y p o t h e s i s i s se t up t h a t t h e s e
measured s t r e r q t h coula h ~ v e come f rom a p o p u 1 a t ; i o n witP
some speci t ic mean va.Lui? ( m ) which i s t h e C y l i n d e r s t r e n g t h ,
To ties t:, t h i s h y p o t h e s i s , we s h a ? ? employ t-tes t , which
dcL31s sit!? the $ ? s t . i n r ~ t l l > n of a t r u e v a l u e from a s a m p l e
and t h e sstabXishing of the C o n f i d e n c e r a n q e s w i t h i n which
I- ... !- le .. true value c a n b e s a i d tcl l i e , Before t h e c a l c u l a t i o n
i.:; made, howeser, sofie signlf icance l e v e l r e p r e s e n t i n g t h e
a c c e p t a b l e r i s k a£ rni.l1ci;xj an error s h o ~ l d be d e c i d e d u p o n ,
for t h e r e j i x t i o n of t h e n u l l h y p o t h e s i s ,
If t h e t :abul . i ted value of t for this l e v e l is e x c e e d e d ,
t h e n h y p c 3 t h e s i s can be rejected - t h e h o l l o w b l o c k g r o u p
g i v i n g a mean ( 2 ) c a n be s a i d n o t t o have come f rom a
p o p u 2 a t i o n w i . t h a incan o f ( m ) - w i t h t h e a c c e p t e d r i s k o f
b e i n g wrong,
For t h e g r o s s a r e a s t r e n g t h , t h e h y p o t h e s i s t h a t t h e
h o l l o w b l o c k g r o u p mean s t r e n g t h is a n e s t i m a t e o f t h e
t r u e p o p u l a t i o n mean ( m ) i s not t r u e . T a b l e 4.2.3 shows
the r e s u l t o f t-test f o r t h e n e t area mean s t r e n g t h for
t h e four h o l l o w b l o c k types. We se t up the h y p o t h e s i s
that t h e t r u e mean i s equal t o t h e s p e c i f i e d v a l u e m ,
H = m 0
and t h e correspol?dirrq t equat ion is
w h e r e x is t he nean of tP:e sample; m p o p u l a t i o n specific
mean v a l u e ; and S i x ; i s d e s i g n a t e s t h e e s t i m a t e d s t a n d a r d
d e v i a t i o n of tnb? mearls or samples of size n d r a w n f rom the
p o p u l a t i o n 1wh i.ch i s es tiroa ted t o h a v e a s t a n d a r d d e v i a t i o n S ( X ) / ~ *
of s(x1, an12 are r e l a t e d in the following way: S(?)=
The c a l c u l a t e d valt ic of t does not exceed the t a b u l a t e d
value at t h e significance l e v e l a t which we had dec ided t o
rejscl: k h e hypo thcsi:;. Only t he ejs-cas.t: net: ,3rc,.t mear.
s t r e n g t h of 3QH12.5-30H60 s a t i s f Led the c o n d i t i o n , We
s h a l 1 a c : q ~ t t.Pie I:ypo th~~si:; t h s t if s rne,in :j t r e i ~ g t h i:;
equal to t h e Cyl inder mean s t r e n g t h ,
For t h e ct:t?::lr as-cast net: a r e a mean s t r e n g h t s , t h e
calcul .a ted t v a l w s exceeded the tabulated values a t 0.02
s i s n i , f i cancc l e v e l a n d w& shall r e j ec t t h e hypothesis,
We s h a l l accept t h e hypat.hesis t h s t the net area mean
s t rer iy tt:s of 40,7H12.5-:10,?H60, SOH12,5-SOH50 and 6UH12.5-
6GM45 h > > l l o w blocks i s I I c J ~ equal t o t h e c y l i n d e r mean
t m 5.709, f o r 3Gr! %Ze5-3W!6Q blocks is yrea ter than t h e a
t abu lakc5 tn ,02 , ? 4 = 2 , C 3 8 , and so we s h a l . 1 r e j e c t t h e
hypothe,.l;is t h a t i t c n e t are?). mean s t r e n g t h is equal to the
cy l i fnuc t s t r e n g t!-i, We shaiI accept t h e h y p o t h e s i s t h a t i t
is greater than cylinder s t renyth*
Fc;,r L?8,7iil2,5-4G. ' ' 360 , SOH:!%, 5--SOH60 and 60H12.5-69H45
holi.czw blocks t es ted on side surface, the cafculsted
t: --; 2.1.25, 2.528 and 2A.68 do not. exceed t he t abu l . a t ed
to,O2,?-2,821., 2.321 .ric to.02,11:2,71€3 r c s p e c t i c e l y , We
s h a l l a c c e p t t h e h y p o t h e s i s t h a t t h e i r v a r i o u s n e t a rea mean
s t r e n g t h s i s e q u a l t:o t h e C ' y l i n d e r s t r e n g t h .
From t h i s , w e c o n c l u d e t h a t t h e c m p r e s s i v e s t r e n g t h
of 30H12.5-30H60 h o l l o w blocks i s be t t e r ccilculatea o n t h e
bas i s of n c t a rea of as-cast s u r f a c e . For 40.7H12.5-40.7H50,
50H12.5-50W60, a n d 6Otll2,'5-6OH45, t h e Compressive s t r e n g t h
is better calculated o n bas is of n e t area of t h e side s u r f a c e
c o m p r e s s i o n tcst a t 0.02 s i g n i f i c a n c e l e v e l ,
B u t i p S t r u c t u r a l C o m p r e s s i o n members (e .g . m a s o n r y
w a l l s ) t h e s i t u a t i o n i s s im i l a r t o t h a t e x i s t i n g i n . a test
b l o c k a s - c a s t . A l s o t h e C r u s h i n g l o a d of as-cast s u r f a c e
is g r e a t e r t h a n t h e s i d e s u r f a c e c r u s h i n g load. T h e s i d e
s u r f a c e c r u s h i n g load i s a b o u t 48.8%-81,6% of t h e as-cast
s u r f a c e c r u s h i n g load, I n terms o f load c a r r y i n g c a p a c i t y ,
compression tcst o n a s - c a s t s u r f a c e is better.
T h e s i d e s u r f a c e net- a r e a i s s m a l . l e r t h a n t h e as-cast
s u r f a c e n e t area. T h e side s u r f a c e net a r e a s t r e n g t h i s
g r e a t c r t h a n t h e as -cas t s u r f a c e s t r e n g t h , R u t t h e c r u s h i n g
load ol' side s u r f a c e of E! block is less t h a n t h e c r u s h i n g
load of as-cast s u r f a c e , When t h e side s u r f a c e n e t a r e a
s t r e n g t , h i s u s e d t o c a l c u l a t e t h e c r u s h i n g l o a d of b l o c k
based o n t he as-cast: s u r f a c e n e t a rea , . t h e c r u s h i n g load,
o b t a i n e d i s great.er t h a n t h e a c t u a l C r u s h i n g load of t h e
as-cast tested b l o c k . T h e r e f o r e , there is d a n g e r o f o v e r -
e s t i m a t i o n of t h e C . r u s h i n g load, by u s i n g i n a p p r o p r i a t e
n e t area.
A l s o i n m a s o n r y p r i s m tests, t h e b l o c k s are l a i d
as-cast i n s tack b o n d , i n o r d e r t o o b t a i n t h e c h a r a c t e r i s -
t i c c o m p r e s s i v e s t r e n g t h (fk) of m a s o n r y w a l l . When s h e l l
b e d d i n g is u s e d i n c o n s t r u c t i n g h o l l o w s a n d c r e t e m a s o n r y
w a l l , t h e d e s i g n s t r e n g t h of t h e wall is t h u s e q u a l to t h e
c h a r a c t e r j . s t i c c o m p r e s s i v e s t r e n g t h f k o f t h e w a l l mu1 t i p l i e d
b y a factor e q u a l to t h e b e d d e d a r e a d i v i d e d b y t h e g r o s s
area"). U s i n g t h e s i d e s u r f a c e n e t area s t r e n g t h as t h e
C o m p r e s s i v e s t r e n g t h of h o l l o w b l o c k c o n t r a d i c t s t h e a b o v e
o b s e r v a t i o n , s i n c e , t h e s i d e s u r f a c e n e t area d o e s " n o t come
i n c o n t a c t w i t h mortar b o t h i n e x p e r i m e n t a l a n d a c t u a l
c o n s t r u c t i o n , ,
The l i n e a r c o r r e l a t i o n b e t w e e n t h e s i d e s u r f a c e n e t
a r e a s t r e n g t h and t h e a s - c a s t s u r f a c e n e t area s t r e n g t h
p r o v i d e s a good c o n d i t i o n f o r t h e u s e of s i d e s u r f a c e n e t
a r e a s t r e n g t h as t h e C o m p r e s s i v e s t r e n g t h of b l o c k , T h e
a s - c a s t s u r f a c e n e t area s t r e n g t h c a n e a s i l y be e s t i m a t e d .
4.3.0 COMPARISON OF AS-CAST SURFACE STRENGTH A N D SIDE SURFACE STRENGTH OF HOLLOW SANDCRETE BLOCKS,
C o m p r e s s i o n tests o n S a n d c r e t e h o l l o w b l o c k s h a v e
b e e n l imi ted to as-cast s u r f a c e s . T h e o t h e r tvm s u r f a c e s :
end s u r f a c e a n d s i d e s u r f a c e h a v e been t h o u g h t t o be of
Lit t le significance since no a p p l i c a t i o n is made u s e of
them. B e c a u s e o f t h i s , C .ompress iva s t r e n g t h of h o l l o w
b l o c k s h a s been c a l c u l a t e d o n t h e b a s i s of t h e g e o m e t r y
of t h e as-cast s u r f a c e ,
I n S t r u c t u r a l c o m p r e s s i o n members ( m a s o n r y w a l l s )
t h e sf t u a t l o n :i.s s i m i l a r to t h a t e x i s t i n g . i n a t es t
block as-cast, This ciaKes as-cast tested blocks a mere
real i s t i c c a m p r e s s i o n test. fo r s a n d c r e t e h o l l o w b l o c k s .
.It is good to p o i 2 t o u t . t h e most i m p o r t a n t f a c t o r
m i l i t a t i n g a < , - ; , i n s t b locks tested as-cast: - l a c k o f smooth-
ness and planeness, L a c k o f p l a n e n e s s c a n l o w e r t h e
s t r e n g t t l of material, Tbi s phenomenon is associated w i t h
t h e as-cast surfaces of a n y moulded m a t e r i a l l i k e h o l l o w
s a n d e r e t e blocks.
'PJ avoi.d this l o s s of s t r e n q k i l , p l a n e and srnooth
surfaces a r e essential. T h e r e are three neans of o v e r -
coming t h e i l l - e f f e c t s of uneven e n d surfaces ~f the
specimen: c a p p i n g , g r i n d i n g and packi.r.y w i t h a b e d d i n g
ma te r i a l . NIS-75 requires t h e as-cast surfaces of a s a n d -
crete b l o c k t o be c a p p e d w i t h i .nor tar mix r a t i o of 1: '1
a n d w a t e r / c e r n e n t r a t i o n o t less t h a n 0.35,
C a p p i n g has t h e c f f e c t of i n c r e a s i n g s t r e n g t h b y
12-15 %. Thomas and Chinsma,n o f F o u r a h Bay C o l l e g e 21
recommended r u b b i n g down t h e test f a c e s w i t h c a r b o r u n d u m
p l a t e wiLh ca re t o a c h i e v e t h e e v e n s u r f a c e s ,
To o v e r c o m e t h e e x t r a work i n v o l v e d i n c a p p i n g
o p e r a t i o n , c o m p r e s s i o n tests were d o n e on t w o p e r p e n d i c u l a r
swfaces* of h o l l o w b l o c k s : as-cast surface ( 2 - s u r f ace) a n d
the s i d e surface ( x - s u r f a c e ) . T h e s i d e s u r f a c e s of h o l l o w
bZocks do not l a c k s m o o t h n e s s and p l a n e n e s s . T h e u s e f u l -
ness of s a n d c r e t e h o l l o w i n t h a t p o s i t i o n is n o t known
except w h e r e l o c a l c o n t r a c t o r s and masons u s e s o l i d
450mm x 150mm x 225mm s a n d c r e t e b l o c k s i n t h a t p o s i t i o n
w h i l e . l a y i n g t h e f o u n d a t i o n b l o c k w a l l s .
When s o l i d b l o c k s (450x~50x225mm~ are u s e d i n s u c h
position, the aspect ratio becomes 0,667 i n s t e a d o f 1.5
and aspect r a t i o i n f l u e n c e r t h e s t r e n g t h o f block. But
same for as-cask and side s u r f a c e s and is equal ta u n i t y .
It. i.s a l so n e c e s s a r y to p o i n t out t h e d i f f e r e n c e i n
t h e p o s i t i o n o f c a v i t i e s i n t h e h l o c k s b e i n g tested w h i c h
i n f l u e n c e s the f a i l u r e p a t t e r n o f t h e c c m p r e s s i o n tests
on t h e t w c s u r f a c e s . I n a s - c a s t s u r f a c e , t h e h a l l o w o p e n s
o u t a t t h e t w o p a r a l l e l as-cast s u r f a c e s , w h i l e i n t h e
s i d e s u r f a c e s , t h e h o l l o w is h i d d e n i n b e t w e e n t h e two
p a r a l l e l s i d e s u r f a c e s .
I n t h e as-cast test, c r a c k s a p p e a r i n t h e face s h e l l
and end-webs see p l a t e 4.3.1. C o l l a p s e o c c u r s when
s u f f i c i e n t c r a c k s h a v e b e e n f o r m e d a t maximum l o a d w i t h i n
t h e f a c e s h e l l s a n d webs. C o m p r e s s i o n test o n s i d e
s u r f a c e showed t h a t cracks are i n i t i a t e d i n t h e c e n t r e -
. web, a n d k t maximum c r u s h i n g l o a d , t h e face s h e l l c a v e s
i n t o t h e h o l l o w . See p l a t e 4.3.2
I n t h e a b s e n c e of c e n t r e - w e b , side s u r f a c e t e s t e d
h o l . 1 0 ~ b l o c k s p r o d u c e e x p l o s i v e s o u n d a t t h e p e a k c r u s h i n g
l o a d and a l s o p u t s t h e s teel p l a t e u s e d to d i s t r i b u t e t h e
l o a d o u t o f p l a n e . A l s o n o t i c e a b l e is t h e c h a n g e i n t h e
s o u n d o f t h e c o m p r e s s i o n m a c h i n e a t t h e p e a k o f t h e c r u s h -
i n g l o a d ; w i t h t h e l o a d i n d i c a t o r s t a t i o n a r y a t t h e
maximum c r u s h i n g load f o r some s e c o n d s u n t i l f a i l u r e o c c u r s .
T h i s phenomenon was o b s e r v e d fo r a l l t h e 60H12.5 - 60H45
b l o c k t y p e s t e s t e d o n t h e s i d e s u r f a c e . T h i s may b e
a t t r i b u t e d to t h e s k e l e t a l n a t u r e o f t h e f a c e s h e l l a n d
t h e cross m b s .
To e x p l , o r e , t h e good p o t e n t i a l s o f t h e s i d e s u r f a c e s
o f h o l l o w b l a c k s , s t a t i s t i c a l a n a l y s i s was u s e d t o e s t a b l i s h
-1 APPEARANCE OF CRACKS AS HOLLOW IS TESTED O N SIDE SmFACE
t h e c o r r e l a t i o n between t h e s t r e n g t h s measured on t h e
two p e r p e n d i c u l a r s u r f a c e s . A n a l y s i s of test d a t a from
f o u r d i f f e r e n t b lock t y p e s shown i n t a b l e 4 .1 g a v e t h e
f o l l o w i n g l i n e a r r e g r e s s i o n e q u a t i o n s f o r t h e c o r r e l a t i o n
between t h e s t r e n g t h s f and f based on t h e i n d i v i d u a l 'ig 29
s t r a i g h t l i n e s f o r e a c h b l o c k group. T h i s i s shown i n
f ig (4 .3 .1 ) .
For 30H12.5 - 30H60 b l o c k s
f = - 2.5938 + 1.5261 f ---- xg
(4.3.1) 29
2 ( r = 0.907 s t a n d a r d e r r o r = 0.148N/mm. )
For 40.7Hl2.5 - 40.7H60 b l o c k s
f = - 4 . 3 1 6 2 + - 2 . 2 0 8 2 f ---- xg =g
(4.3.2)
2 ( r = 0.964 s t a n d a r d error = 0.080N/mm
For 50H12.5 - 50H60 b l o c k s
2 ( r = 0.855 s t a n d a r d error = 0.109N/mm )
For 60H12.5 - 60H45 b l o c k s
(r = 0.996 s t a n d a r d e r r o r = 0 . 0 2 6 ~ / , , ~ )
The c a l c u l s t e d v a l u e o f r , 0.907 f o r 30H12.5 - 30H60
b l o c k s is compared w i t h the v a l u e g i v e n i n Appendix B
( t a b l e 3 . 2 1 ~ ~ . I t e x c e e d s t h e t a b u l a t e d v a l u e o f 0.878
a t 0.05 p r o b a b i l i t y l e v e l b u t i t less t h a n 0,934 a t 0.02
l e v e l , w e c a n s a y with 95 p e r c e n t c e r t a i n t y b u t n o t w i t h
Tab le 4-7.0 As-Gist SurFncc Gross Area Strcrrgth and S i d e Surface Grcss Area S t r e n g t h 05 Hollow Sarldcrete Block.;,
- B l o c k Type
As-Cast Gross -
S i de-Surf 'ice Area S t r e n g t h i ( i\S/mm2)
::g
LEGENO 30%HOLLOW BLOCKS
I 2.0 3:0 4 0 AS-CAST SURFACE STRENGTH frq I N h m 2 1
98 p e r c e n t c e r t a i n i t y t h a t t h e r e i s a l i n e a r carrel-ation,
The c a l c u l a t e d v a l u e of r , 0.964 f o r 40.7H12.5-
40.7H60 b locks exceeds t h e t a b u l a t e d v a l u e of 0.959 a t
0.01 l e v e l b u t i s less t han 0.991 a t 0.001 l e v e l , we
can s ay wi th 99 p e r c e n t c e r t a i n i t y b u t not wi th 99.9
p e r c e n t c e r t a i n i t y t h a t there is a l i n e a r c o r r e l a t i o n .
T h e c a l c u l a t e d v a l u e of r , 0.855 f o r SOH12.5-SOH60
b locks exceeds t h e t a b u l a t e d v a l u e of 0.805 a t 0.1 l e v e l
b u t i s less t h a n 0.878 a t 0.05 l e v e l , w e can s a y w i t h
90 p e r c e n t c e r t a i n i t y b u t n o t wi th 95 p e r c e n t c e r t a i n i t y
t h a t t h e r e i s a l i n e a r c o r r e l a t i o n .
The c a l c u l a t e d v a l u e of r , 0.996 f o r 6OH12.5-60H45
b locks , exceeds t h e t a b u l a t e d v a l u e o f 0.990 a t 0.01
l e v e l b u t less than 1.00 a t 0.001 l e v e l , w e can s ay w i t h
99 p e r q e n t c e r t a i n i t y b u t no t w i th 93.9 p e r c e n t c e r t a i n i t y
t h a t there i s a l i n e a r c o r r e l a t i o n .
When a l l t h e i n d i v i d u a l s l o p e s a r e pooled i n t o a
s i n g l e s l o p e f ig (4 .3 .21 , t h e l i n e a r r e g r e s s i o n e q u a t i o n
between t h e s t r e n g t h s f and f becomes: xg =g
f = - 0.3824 + 0.8332 f ---- x'3 =g
(4.3.5)
2 (r = 0.921 s t a n d a r d e r r o r = 0.265N/mm 1.
The v a l u e of r , 0.921 exceeds t h e t a b u l a t e d v a l u e of 0.708
a t 0.001 l e v e l and we c a n s ay wi th more than 99.9 p e r c e n t
LEGEND " / . /
/
3 0 % I-tOLLOW B L O C K S 0 / 5 2
/ /
1
T
;o 3% 43 As-cAsf SURFACE s TRENcTH rzq i ~ / ~ ~ ~ 1
c e r t a i n i t y t h a t t h e r e i s a s i n g l e s l o p e l i n e a r c o r r e l a t i o n .
A h i g h d e g r e e o f l i n e a r c o r r e l a t i o n e x i s t s b e t w e e n t h e
s i d e s u r f a c e g r o s s a r e a s t r e n g t h ( f a n d as-cast s u r f a c e xg
g r o s s area s t r e n g t h (f a s i n d i c a t e d by t h e c o r r e l a t i o n z 9
c o e f f i c i e n t s shown i n t h e p r e c e d i n g e q u a t i o n s . T h e sum
of s q u a r e s o f d e v i a t i o n f rom t h e b e s t s t r a i g h t l i n e t h r o u g h
e a c h s e t of d a t a s e p a r a t e l y i s 0 .121797578, w h i l e t h e sum
of s q u a r e s o f d e v i a t i o n f r o m t h e G . e s t s t r a i g h t l i n e t h r o u g h
a l l t h e 9 d a t a is 1.191389506. We c a n c o n c l u d e t h a t t h e
l i n e a r c o r r e l a t i o n b e t w e e n t h e s t r e n s t h f a n d f . c a n xg z 9
be best r e p r e s e n t e d by s t r a i g h t l i n e s w i t h d i f f e r e n t s l o p e .
C o r r e l a t i o n s b e t w e e n t h e g r o s s a r e a s t r e n g t h o f s i d e
s u r f a c e ( f ) a n d the n e t area s t r e n g t h ( f z n ) of as-cast xg
s u r f a c e a r e shown i n f i g 4,.3.3, 4-3.4 and 4.3.5. R e g r e s s i o n
C u r v e s shown i n f i g 4.3.3 w e r e o b t a i n e d b y u s i n g i n d i v i d u a l
slopes a n d h a v e t h e f o l l o w i n g r e g r e s s i o n e q u a t i o n s :
F o r 30H12.5 - 30H60 b l o c k s
( r = 0.907 s t a n d a r d error = 0 . 1 4 8 ~ / m r n ~ )
F o r 40.7H12.5 - 40.7H60 b l o c k s
(r = 0.966 s t a n d a r c l ' e r r o r 0 . 0 8 0 ~ / m m ~ )
F o r 5 0 3 1 2 - 5 - SOH60 b l o c k s
Table 4.3,l As-Cast Surface X e t Area Strength and S i d e Surface Gross Area Strength of Holl,w Sandcretc H l x k s .
H l o d c T w U = t Face S h e l l C
r Thickness e ( t 1
v d I
AS-Cask Gross A r m S t r e n g t h
2 zn (N/m 1
S i d e Surface !;row Area
BLOCKS "
A S - Z ~ ~ T -FACE ' ~ ' ~ R E N G W dS&p?l s.25 *
FG4.3.3 RELATION BETWEEN STRENGTH3 &gM &
2 ( r = 0.856 s t a n d a r d error = 0.109N/mm )
F o r 60H12.5 - 60H45 b l o c k s
( r = 0.996 s t a n d a r d e r r o r = 0 . 0 2 6 ~ / m m ~ )
The c v r r e l a t i o n c o e f f i c i e n t s a n d s t a n d a r d errors
shown i n t h e a b o v e e q u a t i o n s a r e t h e same w i t h t h e c o r r e l a -
t i o n c o e f f i c i e n t s a n d s t a n d a r d errors o b t a i n e d i n t h e
c o r r e l a t i o n e q u a t i o n s b e t w e e n s t r e n g t h f and f and xg z g '
. t h e same ' p r o b a b i l i t y l e v e l is m a i n t a i n e d .
T h e bes t s t r a i g h t l i n e t h r o u g h a l l t h e d a t a ' i s shown
i n f i g 4.3. a n d t h e r e g r e s s i o n e q u a t i o n i s g i v e n as:
L ( r = 0.911 s t a n d a r d error = 0.171N/mm )
I t s p r o b a b i l i t y l e v e l is t h e same a s t h a t g i v e n b y
e q u a t i o n 4.3.5.
I f i n d i v i d u a l l i n e s shown i n f i g ( 4 . 3 . a r e d r a w n
w i t h t h e same s l o p e , 0 ,7813 , w e s h a l l o b t a i n t h e f o l l o w i n g
r e g r e s s i o n e q u a t i o n s f o r t h e c o r r e l a t i o n b e t w e e n g r o s s
a r e a s t r e n g t h o f t h e s i d e s u r f a c e and n e t area s t r e n g t h
o f t h e a s - c a s t s u r f a c e :
F o r 30W12.5 - 30H60 b l o c k s
f = - 1 .1883 + 0.7813 f z n ---- (4 .3 .11) x g
2 ( r = 0.880 s t a n d a r d e r r o r 0.171N/mm )
For 40.71.112.5 - 40.7H60 b locks
f = - 1.9665 + 0.7813 f z n ---- x g
(4.3.12)
2 ( r = 0.0883 s t a n d a r d error = 0.143N/rnm
F o r 50H12.5 - 50H60 b locks
f = - 1.8759 + 0.7813 f ---- X g zn (4.3.13)
2 ( r = 0.481 s t a n d a r d e r r o r 0.185N/rnm )
For 60H12.5 - 60H45 b locks
f = - 1.8963 + 0.7813 f z n ---- xg
(4.3.14)
2 ( r 2 0.978 s t a n d a r d e r r o r = 0.059N/mm )
For 30H12.5 - 30H60 and 40.7H12.5 - 40.7H60 b locks ,
the c a l c u l a t e d r , 0.880 and 0.883 exceeded t h e t a b u l a t e d
r ,0 .878 a t 0.05 l e v e l bu t less than 0.934 a t 0.02 l e v e l ,
and w e can s a y w i t h 95 p e r c e n t c e r t a i n i t y b u t n o t w i t h
98 p e r c e n t c e r t a i n i t y t h a t there is a pooled s l o p e
1 inear . c o r r e l a t i o n .
For 50H12-5 - 50H60 b l o c k s , t h e v a l u e of r , 0.481
is less t han t h e t a b u l a t e d r , 0.805 a t 0.1 l e v e l , w e
c an s a y wi th less than 90 p e r c e n t c e r t a i n i t y t h a t t h e r e
is a pooled s l o p e l i n e a r c o r r e l a t i o n between s t r e n g t h
" a n d f z n . ~9
For 60H12.5 - 60H45 b locks , t h e r v a l u e o f 0.978
exceeds t h e t a b u l a t e d r v a l u e o f 0.950 a t 0.05 l e v e l ,
b u t less than 0.980 a t 0.02 l e v e l , w e c an say wi th 95 per-
BLOCKS *
n
v
"$25 ?E~&sT SURF% S T T R N G T ~ ? ' < ~ I N ~ ~ ) b25 + FG4.35 POOLED SLOPE RELATION BETWEEN STRENGTHS fxq AND ';-,
c e n t c e r t a i n i t y b u t n o t w i t h 98 p e r c e n t c e r t a i n i t y t h a t
t h e r e i s a l o o p e d s l o p e l i n e a r c o r r e l a t i o n b e t w e e n
s t r e n g t h f a n d fZ, o f 60H12.5 - 60H45 b l o c k t y p e s . xg
I n g e n e r a l , e x c l u d i n g t h e 50H12.5 - 50H60 b l o c k
t y p e s , we c a n s a y w i t h 9 5 p e r c e n t c e r t a i n i t y b u t n o t
w i t h 98 p e r c e n t c e r t a i n i t y t h a t t h e r e is a l o o p e d s l o p e
l i n e a r c o r r e l a t i o n b e t w e e n b l o c k s t r e n g t h s f a n d fzn. x 9
I t is p e r t i n e n t to c o m p a r e t h e i n d i v i d u a l s l o p e s
u s e d to d e s c r i b e t h e l i n e a r c o r r e l a t i o n b e t w e e n s t r e n g t h s
f a n d x
t o know w h e t h e r :
a ) t h e i n d i v i d u a l s t r a i g h t l i n e s make a s i g n i f i c a n t l y
bet ter c o r r e l a t i o n t h a n o n e l i n e .
b ) a b e t t e r c o r r e l a t i o n r e s u l t i f e a c h o f t h e
i n d i v i d u a l l i n e s i s d r a w n w i t h i t s own s l o p e , or s h o u l d
a l l t h e l i n e s b e d r a w n w i t h t h e same s l o p e .
a By e x a m i n i n g t h e p l o t o b v i o u s a n s w e r s to t h e q u e s t i o n s
a b o v e c a n b e o b t a i n e d , b u t s ta t i s t ics o f f e r s a q u a n t i t a t i v e
method f o r a n o b j e c t i v e a n a l y s i s o f t h e d a t a . T h e s t a t i s -
t i c a l method35 is t o d e t e r m i n e t h e sum o f s q u a r e s o f
d e v i a t i o n s f r o m t h e best s t r a i g h t l i n e t h r o u g h a l l t h e
d a t a , t h e b e s t s t r a i g h t l i n e t h r o u g h t h e i n d i v i d u a l sets
w i t h a p o o l e d e s t i m a t e o f t h e s l o p e . a n d t h e b e s t s t r a i g h t
l i n e t h r o u g h t h e i n d i v i d u a l sets, e a c h w i t h i t s own s l o p e .
T h e c o m p a r i s o n o f each of t h e sums o f s q u a r e s a t i t s d e g r e e
of f r e e d o m w i t h t h e minimum sum o f s q u a r e s from e a c h l i n e
s e p a r a t e l y p r o v i d e s a v a r i a n c e r a t i o which c a n b e tested
b y t h e F test.
C o m p a r i n g , t h e b e s t s t r a i g h t l i n e t h r o u g h i n d i v i d u a l
sets, e a c h w i t h i ts own s l o p e , and t h e best s t r a i g h t l i n e
t h r o u g h a l l t h e d a t a . T h e r a t i o o f "be tween s l o p e s w mean
s q u a re a n d t h e " e r r o r t t mean s q u a r e of 0 .403174495/0 .011072507
= 36 .411 i s t e s t e d a g a i n s t F a t 3 a n d 11 d e g r e e s of f r e e d o m
( A p p e n d i x C t a b l e s 7.8 a n d 7 .9) . The F v a l u e s are ' 3 - 5 9
a t t h e 0.05 l e v e l and 6.22 a t t h e 0 .01 l e v e l i n d i c a t i n g
t h a t w i t h r e s p e c t t o t h e s e d a t a t h e amount. o f d e v i a t i o n s
removed b y u s i n g i n d i v i d u a l l e a s t - s q u a r e l i n e s f o r e a c h
set o v e r t h a t removed by u s i n g b e s t s t r a i g h t l i n e t h r o u g h
a l l t h e d a t a is h i g h l y s i g n i f i c a n t . T h e r e i s less t h a n
1 p e r c e n t c h a n c e o f n o t b e i n g i n error i f a s i n g l e least-
s q u a r e l i n e w i t h s l o p e , 1.2404 is c o n s i d e r e d .
C o m p a r i n g , t h e b e s t s t r a i g h t l i n e t h r o u g h i n d i v i d u a l
se ts , e a c h w i t h i t s own s l o p e , a n d t h e b e s t s t r a i g h t l i n e
t h r o u g h t h e i n d i v i d u a l sets w i t h a p o o l e d est imate o f t h e
s l o p e . The r a t i o o f "be tween s l o p e w mean s q u a r e and t h e
"errorn mean s q u a r . e o f 0 ,045438791/0 .011072507 = 4.104
is t e s t e d a g a i n s t F a t 3 a n d 11 d e g r e e s o f f r e e d o m
(Appendix C tables 7.1 and 7,91. T h e P values a r e 3,59 a t
t h e 0,05 l e v e l and 0.22 a t t h e 0.0l l e v e l i n d i c a t i n g t h a t
w i t h respect to t h e s e da t a , t h e amount of d e v i a t i o n
removed by using i n d i v i d u a l le2at-square l i n e s fo r each
s e t over t h a t removed by using a pooled slope for a l l
t h e sets is s i g n i f i c a n t .
T h e r e i s Less t h a n 5 p e r c e n t b u t more t h a n 1 percent
c h a n c e of n o t ',,ei!.l~ i n e r r D r i f the l i n e s a.re cor~sidered
to h a v c a zornmnn slope, 0.7813,
A l t h o u g h , l ooped ~ i ~ d s i n g l e s lope regress ion l i n e s
showed si .cZjnif i .can t corre l .a t io : .~ c o e f f i ~ i s n t s , the l i n e a r
r e l a t i o n s h i p between t h c gross a rea s t r e n g t h of s i d e
su r face df ) and t h e fie+: area s t r e n g t h of the as -cas t xg
surface (!: ), a uetter linear c o r r e l a t i c i n r e s u l t i f each zn
of t h e i n d i v i d u a l l i n e s is drawn w i t h its awn s l o p e .
We shL2l l now, consider t h e net area strength of s i d e
s u r f a c e (i ) and t h e n e t area strength of t , h e as-cast X rr
s u r f a c e ( f z n ! . F i g 4.3.6 shows t h e best s t r a i g h , t l i n e
through I n d i v i d u a l sets, each with its own s l o p e , They
have the f o l l o w i n g r e g r e s s ion equations:
For 3QH12,S - 30H60 bl.ocks
f = - 6.1764 + 2.5300 f Z n ---- (4,3.15! xn (r = 0.908 s t q n d a r d error = 0.350M/nrn
2
Table 4.3.2 As-Cast b b t Area Strength and Side S u r f a m N e t Area Strength of Hollw Sandcrete Blocks
/ LEGEND / @-------
30% I4OI. L OW
A I 3- - +-- - -- - - <z--.--- $ -- -- - . - --
32 5 3.75 e5- AS-CAST SURFACE STRENGTH tzn l N h m Z )
FIG r9.36 RELATION B E T W E E N STRENGTHS fxn AND fzn
2 ( r = 0.965 s t a n d a r d e r r o r = 0.230N/mm )
For 50H12.5 - SOH60 b locks
xn = - 1.8017 + 1.6049 f z n ----(4.3.17)
Z ( r = 0.055 s t a n d a r d e r r o r = 0.420N/mm )
For 60H12,5 - 60H45 b l o c k s
fxn = - 12.9744 + 4.7988 f z n .--- (4.3.18)
2 ( r = 0.996 s t a n d a r d e r r o r = 0.133N/mm )
The c o r r e l a t i o n c o e f f i c i e n t s a r e t he same wi th
t h e t w b p r e v i o u s s t r e n g t h comparison, and t h e same
d e g r e e of c e r t a i n i t y . D i f f e r e n c e s e x i s t i n s l o p e s ,
i n t e r c e p t s and s t a n d a r d e r r o r s .
Fig(4.3.7) shows t h e b e s t s t r a i g h t l i n e through
a l l t h e d a t a . Also shown a r e t h e 95 p e r c e n t con f idence
l i m i t and 95 p e r c e n t c o n f i d e n c e band of t h e s l o p e is a
f a n ~ s h a p e d a r e a converg ing on t h e mean o f f x n and fzn.
The b e s t s t r a i g h t l e a s t - s q u a r e l i n e is g i v e n by t h e
r e g r e s s i o n equa t ion :
f,,, = - 0.5562 + 1.3423 f z n ---- (4.3.19)
2 ( r = 0.595 s t a n d a r d e r r o r - 0.903N/mm )
The c a l c u l a t e d r , 0.595 exceeds t h e t a b u l a t e d
r , 0.590 a t 0.01 l e v e l b u t lass than 0.708 a t 0.001
l e v e l . We can s ay w i t h 99 p e r c e n t c e r t a i n i t y b u t no t
w i t h 99.9 p e r c e n t c e r t a i n i t y t h a t t h e r e is a s i n g l e
5 3.75 4 2 5 4.75 5.25 *
AS-CAST SURFACE STRENGTHS f t n f N L m 2 1
FIG4.3.7 SINGLE SLOPE RELATON BETWEEN STRENGTHS fxnANDf2n
s l o p e l i n e a r c o r r e l a t i o n between s t r e n g t h s f and f zn. xn But i t h a s modera te c o r r e l a t i o n c o e f f i c i e n t . The h i g h
p r o b a b i l i t y l e v e l depends on t h e d e g r e e o f freedom.
I f t h e i n d i v i d u a l l i n e s shown i n f ig(4 .3 .8) a r e
drawn w i t h a poo led e s t i m a t e o f t h e s l o p e , 2.6377 we
s h a l l o b t a i n t h e f o l l o w i n g r e g r e s s i o n e q u a t i o n s :
For 30H12.5 - 30H60 b l o c k s
f x n = - 6.7034 + 2 . 6 3 7 7 f z n ----(4.3.20)
2 (r = 0.907 s t a n d a r d error = 0.35N/mm
For 40.7H12.5 - 40.7H60 b l o c k s
2 ( r = 0.912 s t a n d a r d e r r o r = 0.374N/mm,)
For 50H12.5 - 50H60 b l o c k s
- 5.8813 + 2.6377 f z n f x n - - ----(4.3.22)
2 (r = 0.655 s t a n d a r d e r r o r ' )
For 60H12.5 - 60H45 b l o c k s
f = - 4.5124 + 2.6377 f a n ----(4,3023) xn 2
( r = 0.747 s t a n d a r d e r r o r = 0.952N/mm
T h e c a l c u l a t e d r , 0.907 and 0.912 f o r 30H12.5 - 30H60 and 40.7H12.5 - 40.7H60 b l o c k s r e s p e c t i v e l y ,
exceeded t h e t a b u l a t e d v a l u e o f r , 0.878 a t t h e 0.05
l e v e l b u t a r e less t h a n 0.934 a t t h e '0.02 l e v e l . For
t h e two t y p e s o f blocks, w e c a n s a y w i t h 95 p e r c e n t
34 3.25 335 4-25 475 5.25
AS-CAST SURFACE STRENGTH I,, IN,+,,^^) FIG4.3.8 POOLED SLOPE RELATION B E T W E E N STRENGTHS fx&NQfm
W 0 5 4.3
/ /
A .. /
/ , LEGEf4D
/ a- 30% HOLLOW BLOCKS
c e r t a i n i t y b u t n o t w i t h 9 8 p e r c e n t c e r t a i n i t y t h a t t h e r e
i s a l o o p e d s l o p e c o r r e l a t i o n ,
F o r t h e 50H12.5 - 50H60 a n d 60H12.5 - 60H45 b l o c k s ,
t h e c a l c u l a t e d r , 0 , 6 5 5 a n d 0 ,747 are less t h a n t h e t a b u -
l a t e d - r , 0 , 8 0 5 a t t h e 0.1 l e v e l , a n d w e c a n s a y w i t h less
t h a n 9 0 p e r c e n t c e r t a i n i t y t h a t t h e r e is a l o o p e d s l o p e
c o r r e l a t i o n b e t w e e n t h e s t r e n g t h s f and f zn of h o l l o w xn
Compar ing , t h e bes t s t r e i g h t l i n e t h r o u g h i n d i v i d u a l
sets, e a c h w i t h i t s - own s l o p e , a n d t h e best s t r a i g h t l i n e
t h r o u g h a l l t h e d a t a . The r a t i o o f " b e t w e e n s l o p e s w mean
s q u a r e a n d t h e "error" means s q u a r e o f 4.267525592/0,9658988
= 44.182 is t e s t e d a g a i n s t F a t 3 and 11 d e g r e e s o f f r e e d o m
( A p p e n d i x C t ab les 7.8 a n d 7.9). The F v a l u e s are 3.59 a t
t h e 0 - 0 5 l e v e l a n d 6 - 2 2 a t t h e 0 - 0 1 l e v e l i n d i c a t i n g t h a t
w i t h r e s p e c t t o t h e s e d a t a t h e amount of d e v i a t i o n s removed
b y u s i n g i n d i v i d u a l l e a s t - s q u a r e l i n e s for e a c h set o v e r
t h a t removed b y u s i n g best s t r a i g h t l i n e t h r o u g h a l l t.he
d a t a i s h i g h l y s i g n i f i c a n t - T h e r e i s less t h a n 1 p e r c e n t
c h a n c e o f n o t b e i n g i n error i f a s i n g l e l e a s t - s q u a r e l i n e
w i t h s l o p e 1,3423 is c o n s i d e r e d .
Compar ing , the best s t r a i g h t l i n e t h r o u g h i n d i v i d u a l
sets, e a c h w i t h i t s own s l o p e , a n d t h e best s t r a i g h t l i n e
t h r o u g h t h e i n d i v i d u a l sets w i t h a p o o l e d estimate o f t h e
s l o p e , The r a t i o of " b e t w e e n s l o p e w mean s q u a r e a n d t h e
" e r r o r w mean squa re of 0.552629253/0.U9658988 = 5.'/%1
i s t e s t e d a g a i n s t F v a l u e s a t 3 and 11 d e g r e e s of f reedom
(Appendix C tables 7.8 and 7.9). The F v a l u e s a r e 3 .59
a t t h e 0.05 l e v e l and 6.22 a t t h e 0.01 l e v e l , i n d i c a t i n g
t h a t w i t h r e s p e c t to t h e s e d a t a t h e amount o f d e v i a t i o n
removed by u s i n g i n d i v i d u a l l e a s t - s q u a r e l i n e s fo r each
set, over t h a t removed by u s i n g a p o o l e d s l c p e f o r a l l
t h e sets i s s i g n i f i c a n t . T h e r e is less t h a n 5.0 p e r c e n t
b u t more t h a n 1 p e r c e n t c h a n c e of not b e i n g i n error if 9
t h e l i n e s a re c o n s i d e r e d to have a common s l o p e , 2.63'17,
A l though , l o o p e d and s i n g l e s l o p e r e g r e s s i o n l i n e s
showed m o d e r a t e c o r r e l a t i o n C o e f f i c i e n t s , t h e l i n e a r
r e l a t i o n s h i p be tween t h e n e t area s t r e n g t h of s i d e s u r f a c e
( f x n ) and t h e net area s t r e n g t h of t h e a s - c a s t s u r f a c e
( f n 1, a b e t t e r l i n e a r c o r r e l a , t i o n r e s u l t i f e a c h of t h e ~n
i n d i v i d u a l l i n e s is drawn w i t h i t s o w n s l o p e .
F ig(4 .3 .9) shows the b e s t s t r a i g h t l i n e t h rough
individual set, each w i t h i t s awn s lope , for c o r r e l a t i o n
be tween s i d e surface c r u s h i n g l o a d and a s - c a s t s u r f a c e
c r u s h i n g load ( P 1. The l e a s t - s q u a r e l i n e s h a v e t h e f o l l o w i n g Z
r e g r e s s i o n e q u a t i u n s :
For 3QH12.5 - 30WbU b l o c k s
(r = 0.9US/ s t a n d a r d error = 8.933 KN)
7 2 F o r 40.7H12.5 - 40.7H60 b l o c k s
(r = 0.965 s t a n d a r d e r r o r = 8.092KN)
F o r 50H12.5 - 50H60 b l o c k s
Px - - - 48 .7461 + 0.8563Pz -------.-- 4 3 - 2 6 )
( r - 0.855 s t a n d a r d error = 11.057KN)
F o r 60H12.5 - 60H45 b l o c k s
( r = 0.996 s t a n d a r d e r r o r = 2,701KN)
The c o r r e l a t i o n c o e f f i c i e n t is t h e same as t h a t shown
by t h e s t r e n g t h c o r r e l a t i o n . T h e o n l y d i f f e r e n c e i s t h e
a b s e n c e of c r i s s - c r o s s i n g .
F u r t h e r more, w e s h a l l t e n d to r e d u c e t h e v a l u e o f
u n e x p l a i n e d v a r i a t r o n a n d i m p r o v e t h e c o r r e l a t i o n b e t w e e n
s t r e n g t h s o n t h e two P e r p e n d i c u l a r s u r f a c e s . T h e un-
, e x p l a i n e d v a r i a t i o n is d u e to random E l u c t u a t i o n o r to
a d d i t i o n a l v a r i a b l e s n o t c o n s i d e r e d , To d o t h i s , we s h a l l
employ m u l t i p l e c o r r e l a t i o n t h e o r y .
M u l t i p l e c o r r e l a t i o n i s t h e d e g r e e o f r e l a t i o n s h i p
e x i s t i n g b e t w e e n t h r e e o r more v a r i a b l e s , T h i s w i l l h e l p
to e l i m i n a t e t h e i n f l u e n c e o f a d d i t i o n a l v a r i a b l e s n o t
c o n s i d e r e d i n t h e s i m p l e l i n e a r c o r r e l a t i o n .
However, some p r i m a r y f a c t o r s af f e c t i n y s t r e n g t h may
i n f l u e n c e t h e c o m p r e s s i o n tests o n t h e two p e r p e n d i c u l a r
s u r f a c e s t o a d z f t e r e n t d e g r e e : f o r i n s t a n c e , t h e c e n t r e -
web t o end-web r a t i o s h a v e v a r i e d i n f l u e n c e c n t n e
s t r e n g t h o f b l o c k s . They are responsible f o r , t h e o v e r a l l
g e n e r a l d i s t r i b u t i o n o f t h e s t r e n g t h i n a n y h o l l o w b l o c k ,
A better C ' o r r e l a t i o n b e t w e e n t h e s t r e n g t h s o n t h e two
p e r p e n d i c u l a r s u r f a c e s may be i m p r o v e d b y t h e inclusion of
t h e C e n t r e - w e b t o end-web r a t i o ( u ) b y u s i n g m u l t i p l e
C o r r e l a t i o n a n a l y s i s , T h e r e l a t i o n b e t w e e n t h e s i d e
s u r f a c e s t r e n g t h a n d t h e c e n t r e - w e b t o end-web r a t i o is a
p a r a ~ o l i c f u n c t i o n , The m u l t i p l e r e g r e s s i o n f u n c t i o n i n
t h i s case i s o n e w h i c h comDines a l i n e a r f u n c t i o n w i t h a
c u r v i l i n e a r f u n c t i o n to e s t a b l i s h t h e C o r r e l a t i o n b e t w e e n
s t r e n g t h s o n t h e two p e r p e n d i c u l a r s u r f a c e s a n d t h e c e n t r e -
WeD t o end-web r a t i o (u) r e s p e c t i v e l y ,
. 'l'he g e n e r a l m u l t i p l e r e g r e s s i o n f u n c t i o n is o f t h e
form:
f / 2
= a + a , f a n + a u + a3u ---- z (4-5-28) tc u 0
w h e r e f s t a n a s tor txn a n d f o f t h e s i d e s u r f a c e of xg
b l o c k ; fcU is t h e s t r e n g t h of 100-mmx100-mmx100-mn c u b e
and ao , a l , a., and a3 are c o n s t a n t s t o be d e t e r m i n e d . L
T h e r e s u l t s of t h e m u l t i p l e r e g r e s s i o n a n a l y s i s
b e t w e e n t h e v c ~ r i . a h l c s f xg9 f z n a n d u a re g i v e n below:
( r = 0.959 s t a n d a r d e r r o r = 0.018)
F o r 40.7H12.5 - 40.7H6O b l o c k s
f /feu = - 0.7042 + 0.1955 f z n - 0.0021U ---- xg (4.3.30)
(r = 0.974 s t a n d a r d e r r o r = 0.013)
F o r 50H12.5 - 50H60 b l o c k s
( r = 0.986 s t a n d a r d e r r o r - 0.006)
F o r 60~1i.5 - 601i45 b l o c k s
f x g / f c u = - 0.2924 + 0.1063 f z n - O.UO5UU + 0.0008~~--(4.3.32)
( r = 1.000 s t a n d a r d error = 0.000).
The c o r r e l a t i o n c o e f f i c i e n t 'is h i g h l y s i g n i f i c a n t
when compared w i t h t h e c o r r e l a t i o n c o e f f i c i e n t s g i v e n b y
t h e b e s t s t r a i g h t l i n e t h r o u g h t h e i n d i v i d u a l sets, d r a w n
w i t h fts own s l o p e .
T h e r e s u l t s o f t h e m u l t i p l e r e g r e s s i o n a n a l y s i s
b e t w e e n t h e v a r i a b l e s f x n 9 'zn and U are shown below:
F o r jOH12.5 - 30H60 b l o c k s
2 x J f c u = - 0.1334 + 0.1413 fzn + 0.035OU-0.002OU ---(4.3.33)
( r = 0.958 s t a n d a r d e r r o r = 0.043)
F o r 40.7H12.5 - 40.7H60 b l o c k s
- - 2 xni fcu
- 2.1115 ,+ 0.5862 f z n - 0.0065U-0.0003U ---(4.3.34)
(r = 0.973 s t a n d a r d , e r r o r = 0.038)
F o r 50H12.5 - 50H60 b l o c k s
f / f C U = - 2 xn 6.0173-2-5728 f z n + 0.4879U-0.0376U ---(4.3.35)
( r = 0.986 s t a n d a r d e r r o r = 0.024)
F o r 60H12.5 - 60H45 b l o c k s
- 1.4619+0.5315 f - 0 . 2 5 1 ~ + 0 . 0 0 3 9 ~ ~ - - - - f x n / f c u - - z n (4.3.36)
(r = 1.000 s t a n d a r d e r r o r = 0.00)
The c o r r e l a t i o n c o e f f i c i e n t s a r e h i g h l y s i g n i f i c a n t
when compgred w i t h l i n e a r c o r r e l a t i o n c o e f f i c i e n t s o f
e q u a t i o n s 4.3.20 - 4.3.23. T h e h i g h l y s i g n i f i c a n t
c o r r e l a t i o n c o e f f i c i e n t s i n d i c a t e t h e reduct ion i n t h e
u n e x p l a i n e d v a r i a t i o n i n t h e l i n e a r c o r r e l a t i o n L
T h e s i g n i f i c a n c e o f m u l t i p l e r e g r e s s i o n is t h a t , i t
m e a s u r e s t h e c o r r e l a t i o n c o e f f i c i e n t b e t w e e n t h e s t r e n g t h s
b y t a k i n g i n t o a c c o u n t some o f t h e v a r i a b l e s t h a t a f f e c t
t h e s t r e n g t h o f h o l l o w b l o c k a n d i n t h i s c a s e t h e c e n t r e -
w e b t o end-web r a t i o ( U ) . T h e i n c l u s i o n o f U d e c r e a s e d
t h e f l u c t u a t i o n v a l u e o f u n e x p l a i n e d v a r i a t i o n , t h e r e b y
i m p r o v i n g t h e c o r r e l a t . i o n a n d g o o d n e s s of t h e f i t .
F i n a l l y , w e shal l c o n s i d e r t h e v a r i a t i o n i n t h e
c r u s h i n g l o a d r a t i o s a n d t h e d i f r e r e n c e s i n t h e two p e r p e n -
d i c u l z r s u r f a c e c r u s h i n g loads, a s Shown I n t a b l e 4.3.U.
I t c a n b e o b s e r v e d t h a t c r u s h i n g l o a a r a t i o s a n d d i f f e r e n c e
h a v e n o r e g u l a r t r e n d b u t i t is a c o n s t a n t f o r e a c h p a r t i c u -
l a r h o l l o w b l o c k .
T a b l e 4.3.3 Maximum C r u s h i n g L o a d s PZ a n d Px, T h e i r
Rat ios a n d D i f f e r e n c e s . I
H o l l o w [ AS-CAST I
! SIDE-SURFACE 1 RATIO BLOC^ I CRUSHLNG LOAD ! C R U S H L N G LOAD^ P ~ / Y Type I P ( K N ) i P ( K N )
X
i z t x i
W e c a n now c o n c l u d e t h a t , t h e r e 1s a l l n e a r
C o r r e l a t ~ o n b e t w e e n C o m p r e s s i v e s t r e n g t h s o n t h e t w o
p e r p e n d i c u l d r s u r f a c e s o f a h o 1 l . o ~ S a n d m e t e b l o c k .
T h i s l i n e a r correlation r e p r e s e n t e d b y best s t r a i g h t
l i n e t h r o u g h t h e l n d l v l d u a l sets ot h o l l o w b l o c k s , e a c h
w i t h i t s own s l o p e ,
' I 'hat t h e i n c l u s i o n of t n e c e n t r e - w e b t o end-web
r a t l o (U) i n t h e c o r r e l a t i o n b e t w e e n s t r e n g h t s o n t n e
t w o p e r p e q d i c u l a r s u r f a c e s by m u l t i p l e r e g r e s s i o n
a n a l y s i s i n c r e a s e d t h e correla t ~ o n coetrlclent, T h e r e
b y d e c r e a s i n g t h e u n e x p l a i n e d v a r i a t i o n i n t h e l l n e a r
c o r r e l a t i o n ,
T h e r e i s n o universal c o n s t a n t r a t i o a n d d i f f e r e n c e
b e t w e e n t h e c r u s h i n g l o a d s o n t h e two p e r p e n d i c u l a r
s u r f a c e s . T h e y a r e c o n s t a n t for e a c h h o l l o w block.
4.4.0 EFFECTS O F GEOMLTRY
4 . 4.1 Ek'k'EC'I'S OF' CEN'I'RE-NEB TO END-WEB RATIO
F o u r d i f f e r e n t h o l l o w b l o c k t y p e s s t u d i e d a r e made
w i t h t h e same mix i n o r d e r t ~ : i n v e s t i g a t e t h e e f f e c t of
c e n t r e - w e b to end-web r a t i o (U ) o n t h e C o m p r e s s i v e
s t r e n g t h of h o l l o w s a n d c r e t e b l o c k s , T h e h o l l o w b l o c k s
s t u d i e d c o n s i s t o f 30 , 40.7, 5 0 , a n d 6 0 p e r c e n t h o l l o w
v o l u m e e a c h w i t h v a r y i n g web t h i c k n e s s a n d a c o n s t a n t
f a c e s h e l l t h i c k n e s s .
I n e a c h c o n s t a n t h o l l o w v o l u m e , b l o c k s w i t h 12.5,
25 , 37 .5 , 5 0 and 6 0 mm end-webs were s t u d i e d . T h u s
C e n t r e - w e b t o end-web r a t i o i $ , , n " e c o n s t a n t f o r t h e - f o u r
d i f f e r e n t h o l l o w b l o c k t y p e s . F i g . 3.3*1 shows t h e mould
d e t a i l s f o r t h e d i f f e r e n t h o l l o w b l o c k s i n v e s t i g a t e d .
I n a l l . , there are n i n e t e e n d i f f e r e n t h o l l o w b l o c k s .
See p l a t e 3.
A 1 1 t h e h o l l o w s a n d c r e t e b l o c k s h a v e cores o r c a v i -
t ies w i t h a p p r o x i m a t e l y p a r a l l e l s i d e s , w i t h o n l y a
m i n i m a l r e l i e f a n g l e , T h i s makes f o r t h i c k e r f a c e s h e l l s
and cross webs a t o n e c r o s s - s e c t i o n a l s u r f a c e , t h e r e
p r o v i d i n g f o r a wider bed j o i n t a t t h a t s u r f a c e , a n d
f a c i l i t a t i n g p i c k u p t h e b l o c k . 10
V a r i o u s a s p e c t s o f t h e b l o c k g e o m e t r y w e r e c o n s i d e r e d
so a s t o i d e n t i f y how g e o m e t r y a f f e c t s s t r e n g t h . From
t h e o r e t i c a l c o n s i d e r a t i o n t h e a c t u a l t h i c k n e s s of t h e s o l i d
p a r t of a h o 1 l . o ~ b l o c k is t h e most s i g a i f i c a n t , T h e most
o b v i o u s way i n w h i c h t h i s d i m e n s i o n a r f e c t s s t r e n g t h is
t h a t d u r i n g c o m p a c t i o n u n d e r a g i v e n p r e s s u r e , t h e f r i c -
t i o n a l r e s i s t a n c e b e t w e e n t h e sides of t h e mou ld a n d
ma te r i a l r e d u c e s t h e e f f e c t i v e n e s s 'of t h e c o m p a c t i o n .
. T h i s i s &re p r o n o u n c e d when t h i s d i m e n s i o n 1s small.
T h e s t u d y is aimed a t f i n d i n g t h e minimum o r maximum
s t r e n g t h s f o r t h e d i f f e r e n t h o l l o w block types a n d t h e i r
c o r r e s p o n a i n g c e n t r e - w e b t o end-web ra t ios . From t a b l e
4 i t c a n be s e e n t h a t h i g h c o m p r e s s i v e s t r e n g t h c a n
be s e e n t h a t h i g h c o m p r e s s i v e s t r e n g t h c a n be a c h i e v e d a t
h i g h c e n t r e - w e b t o end-web r a t i o for t h e f o u r d i f f e r e n t
h o l l o w b l ocks t e s t e d .
F i g 4.4. 0 , 4.4. 1 a n d 4.4-2 s h o w t h e e f f e c t
o f c e n t r e - w e b to ena-web o n maximum c r u s h i n g l o a d as-cast
s u r f a c e n e t area s t r e n g t h , s ide s u r f a c e g r o s s area s t r e n g t h
a n d s i d e s u r f a c e n e t area s t r e n g t h r e s p e c t i v e l y . T h e b l o c k
s t r e n g t h s a r e e x p r e s s e d a s t h e r a t i o of s a n d c r e t e c u b e
s t r e n g t h made of t h e same mix . From s t a t i s t i c a l a n a l y s i s
i t was a p p a r e n t m a t c r u s h i n g b a d or s t r e n g t h i s a p a r a b o l i c
r u n c t l o n of t h e c e n t r e - w e b t o end-web r a t l o of a h o l l o w
s a n d c r e t e block.
For , the Crush ing l o a d s , t h e f o l l o w i n g p a r a b o l i c
equations e x i s t f o r t h e d i f f e r e n t h o l l o w block t y p e s t u d i e d .
For 3UHl2.5 - 30HbU bloc^ t y p e s
P,/Pcu = 3.3202 + 0.0865U-~.u034U 2 ---- (4.4.1.1)
( r = U . ~ 3 . 1 s t a n d a r d e r r o r = 0,083)
( r = 0.946 s t a n d a r d error = 0.204)
For 90.7H12,b - 4U.'/HbU blocK t y p e s
P /P - 2.b2.17 + 0.062oU-0,0029U 2 ----
Z cu (4.4.1.3)
( r = 0,996 s t a n d a r d e r r o r = 0 . ~ 1 5 )
tr = 0.974 s t a n d a r a e r r o r = U.u88
For 50H12.5 - 5OHbu b lock t y p e s
= 1.U72'1 + U.'lU66U - U.UUb8U 2
P d P C U ---- (4.4.1.5)
(r = U.yY9 s t a n d a r d e r r o r = 0,014)
PX/PCU = 1 0 lUb8 + 0.1UbbU 2 ---- (4.4.1.b)
( r = 0,888 s t a n d a r d error = 0,125)
For bOH12.5 - 60H45 block t y p e s .
(r = 0.650 s t a n d a r d e r r o r 0.134)
2 PX/PCU
= 1.0837 + 0.1375U - 0.0145U ---- (4.4.1.8)
( r = 0.589 s t a n d a r d e r r o r 0.344)
1( a --- 30"/0 BLQCK;, I F 1 Q I / t- /--*--- 4 0 ..--. 4:
- 3 0 ~ 1 ~ .. IP,1 (2: .I-- m---. -40.7;,,, ,.
I+ / IF1 ma.... - GO?". .. ;P,l be -_.---L- A- A-.. .- - .- - .-50 50'. + ev *. I?] [ g l .
I
...+.-, -'
*- 7- C,O",, .. iy1 7--- 60°/, - ( % I
A
v
0~72&-- 4 6---- CENTRE-WEB TO END-WEB BAT10 (U)
-G?7----
FIG4.4 .0 EFFECT OF CENTRE-WEB TO EM-W ON CRUSHING LOAD
The power regression c u r v e s between ratio of strength
( fz , / fcu and centre-web t o end-web ratio (U) shown i n
f i g 4.4.1 a r e r e p r e s e n t e d by t h e f o l l o w i n g r e g r e s s i o n
e q u a t i o n s :
For 30H12.5 - 30H60 b l o c k t y p e s
f = 0.4685 + 0.0122U - 0 . 0 0 0 5 ~ ~ ---- f z n / cu (4.4.1.9)
( r = 0.951 s t a n d a r d error = O.U12)
2 xg/f cu = 0.2U94 + 0.0211U - 0,0011U ---(4.4.1.10)
. ( r = 0.94'/ s t a n d a r d e r r o r U,U14)
For 40.7H12.5 - 40.7H60 b l o c k t y p e s
2 z n l t c u = 0.4378 + Oe0104U - 0-0005U ---(4.4.1.11)
(r = 0.997 s t a n d a r d error = 0.0024)
2 xg/fcu = 0.1204 + 0.0179U - 0.0011U ---(4.4.1,12)
( r = 0.0967 standard error = 0.010)
For 50H12.5 - SOH60 block types . 2
z n / f c u = O.jbY8 + U*U2Y6W - 0*0023U ---(4.4.1.13)
( r = 0.999 s t a n d a r d error 0.003)
( r = 0 . ~ 8 8 8 s t a n d a r d e r r o r = 0.012)
For 60H12.5 - 60H45 b l o c k t y p e s .
2 ' zn' = 0.3843 + 0.0232U - 0.ODZYU ---(4.4.1.15)
( r = .0.632 s t a n d a r d e r r o r O.U.34)
( r = 0.59U s t a n d a r d e r r o r = 0.U34)
T a b l e 4.4.7
and U.
-- U-t
c - t
C - 13.28
5.64
3.09
1-82
1.18
10.00
4. Of?
?.OO
1 .OO
0.50
?. 60
?.00
1.70
0.40
0.90
5.12
1.56
0.37
0.00
F i g 4.4.2 shows t h e power r e g r e s s i o n c u r v e s
b e t w e e n r a t i o o f s t r e n g t h fx , l fcu and the c e n t r e - w e b
to end-web r a t i o ( U ) and t h e y a re r e p r e s e n t e d by t h e
f o l l o w i n g e q u a t i o n s .
F o r 30H12.5 - 30H60 b l o c k t y p e
2 fxn / ' cu = U.5046 + 0.0516U - U.UO23U ---(4.4.1,1'/)
( r = 0.947 s t a n d a r d e r r o r = 0 , 0 3 4 )
For 4U.Hl2.5 - 4U.'IH60 b l o c k t y p e s
2 t x n / f c y = 0.3632 + 0.Uk118U - U.UU30U ---(4.4.1.18)
( r = 0.967 s t a n d a r d error = 0.030)
For 50Hl2.5 - SOH60 b l o c k t y p e s
( r = U . U 8 8 s t a n d a r d error = 0.046)
F o r 6UH12.5 - 60H45 block t y p e s .
2 fxn ' fcu
= U.5353 + U.U677U - 0.UU'lI.U ---(4.4.1.20)
( r = U.59U s t a n d a r d error = 0 , 1 7 0 )
T h e C ~ r r e l a t i o n C o e r t l c i e n t given by t h e parabol ic
r e l a t i o n s h i p b e t w e e n r a t i o of c r u s h i n g l o a d s a n d t h e
c e n t r e - w e b t o end-web r a t i o i s t h e same a s t h e C o r r e l a t i o n
C.oeff i c i e n t g i v e n by t h e c o r r e s p o n d i n g s t r e n g t h c e n t r e - w e b
t o end-web r a t i o c o r r e l a t i o n . I t is i n d e p e n d e n t o f t h e
a r e a b u t i s d e p e n d e n t o n t h e d i r e c t i o n o f l o a d i n g .
F o r e a c h o f the f o u r d i r t e r e n t h o l l o w b l o c k s s t u d i e d ,
b o t h t h e a s - cas t s u r f a c e s t r e n g t h a n d t h e s i d e s u r t a c e
s t r e n g t h showed a hicjh d e g r e e o f C o r r e l a t i o n w i t n c e n t r e -
web t o end-web r a t i o , B u t , t n e bUH12-5 - bUH45 t y p e ,
s h o w e d moderate d e g r e e o f c o r r e l a t i o n e x i s t s b e t w e e n t h e
s t r e n g t h a n d t h e c e n t r e - w e b t o end-web r a t i o , T h i s is
d u e t o t h e s t r e n g t h v a l u e of t h e 60H3'/.5 h o l l o w b l o c k
H i g h c o m p r e s s i v e s t r e n g t h is a s s o c i a t e d w i t h h i g h
c e n t r e - w e b t o end-web r a t i o a s snown ~ y t h e test r e s u l t s
t ab l e 4:l a n a a e p l c t e a b y t h e r e g r e s s i o n c u r v e s snown i n
r i g s 4-4.0. , 4 - 4 - 1 a n a 4 -4 -2 .. I t i s a n t l c l p a t e d t h a t
t h e r e s h a l l D e mlnlmum c e n t r e - w e b t o ena- we^ ratio.,
S i n c e h o l l o w b l o c k s w i t h z e r o centre- we^ to end-web r a t i o I
s h o w e d l m p r ~ v e m e n ~ I n c o m p r e s s l v e s t r e n g t n o v e r t h e
p r e c e d i n g c o m p r e s s l v e s t r e n g t h s as s h o w n b y some r e s u l t s .
T h i s r e s u l t i s n o t d e p i c t e d b y t h e r e g r e s s i o n curves w h i c h
s h o w o n l y t h e c e n t r e - w e b t o end -web r a t l o s a n d t h e l r
c o r r e s p o n a l n g maxlmurn s t r e n g t h i n e a c h of t h e t o u r d i f f e r e n t
h o l l o w b l o c k t y p e s .
I t h a s b e e n shown I n s e c t i o n 4.3.2, t h a t various b l o c k
s t r e n g t h wnen compared w i t h sandcrete c y l i n d e r s t r e n g t h
s h o w e d t h a t t h e net area s t r e n g t h c a l c u l a t i o n is better
t h a n t h e g r o s s area s t r e n g t h c a l ~ u l ? ~ ~ h n - I + 3 l c 3 s h o w e d
t h a t c o m p r e s s i v e s t r e n g t h i s better t h e
bas i s o f s i d e s u r f a c e n e t area. A l s o , t h e s i d e s u r f a c e
n e t area is t h e sum of t h e c r o s s - s e c t i o n a l areas o f
t h e cross- webs of a h o l l o w blocK. I t a l s o snows t h a t i t
is t n e c r o s s - w e b s a r e a t h a t s u s t a i n s t h e l o a d when s i d e
s u r f a c e is tested i n c o m p r e s s i o n , we s h a l l specify t h e
c e n t r e - w e b to end-web r a t i o s that a r e n e e d e d to achieve
maximum s t r e n g t h 4.n t h e f s u r d i f f e r e n t hollow b l o c k s
s t u d i e d . T h i s i s shown i n t a b l e 4 .4 .2 . Tabl-%!-4..At 2% -1 : Maxlmum Ceo tre-web to End-web Ratio C o r r e s p o n d i n q to t h e M a x i m u m S t r e n q t h
H o l l o w b l o c k types Maximum Centrc-web M a x i m u m 3 t r e n g t h to End-web Ratio f x , ( N / m m )
3UH12.5 - 30H6U 1 2 - 2 0 7.633
T h e end-web v a r y a t t h e same ra te i n a l l t h e h o l l o w
b l o c k typc-xs a n d is r e s p o n s i b l e for t h e d i r r e r e n c e i n t h e
c e n t r e - w e b to end-web r a t i o among t h e v a r i o u s h o l l o w
b l o c k s . Each s a n d c r e t e h o l l o w b l o c k t y p e t e s t e d , h a s
c e n t r e - w e b t o end-web r a t i o t h a t c a n g i v e t h e d e s i r e d
c h a r a c t e r i s t i c s t r e n g t h b e a r i n g i n mind t h e d i f f e r e n c e
i n t h e q u a l i t y of t h e mater ia l as cas t i n t o d i f f e r e n t
s ize m o u l d s ( v i b r a t i o n a n a c o m p a c t i o n ) . --. --.,-------- >
T h e r e are o t h e r p a r a m e t e r s t h a t m u s t be c o n s l a e r e d
w h i l e s p e c i f y i n ? t h e maximum c e n t r e - w e b t o end-web r a t i o
f o r e a c h of t h e f o u r d i f f e r e n t h o l l o w b locks , or a n y
o t h e r h o l l o w block s i z e . T h e s e i n c l u d e workmansh ip a n d
crack d e v e l o p m e n t . 1 t was o b s e r v e d t h a t h o l l o w b locks
w i t h end-web t h i c k n e s s i s s m a l l e r t h a n 2 5 mm are d i t t l c u l t
t o mould. S u c h h o l l o w b l o c k s d e v e l o p c r a c k s w h i l e s t i l l
p l a s t i c .
T h e r e f o r e , 25 mrn minimum value s p e c i f i e d i n NIS-'I5
f o r webs 2nd iace shell t h i c x n e s s e s s h a l l be m a i n t a i n e d ,
s i n c e h o l l o w blocKs w i t h ena-webs e q u a l to 25 mm are easy
t o worK o n , a n d a re tree o f c r a c k s . Hollow blocks w i t n
end-webs e q u a l to 2 5 mm showed good s t r e n g t h development.
One s l d e - e f f e c t comnon to h o l l o w blocks w l t n l a r g e
, ho l lok vo.Lumc b u t wl t n o u t c e n t r e - w e b , i s t h e t e n d e n c y of
t h e face s h e l l t o b u l g e o u t when t h e s a n d c r e t e Is s t i l l
p l a s t i c . T h i s h a p p e n s when t h e mould i s be ing removed.
T h i s p u t s the s i d e surface of t h e h o l l o w block o u t of
p l a n e . lt is common t o a l l .hand moulded l a r g e s i n g l e
h o l l o w sandcreke blocks. The a e s k e t i c v a l u e of masonry
w a l l s c o n s t r u c t e d w i t h s u c h h o l l o w b l o c k s w i l l be i m p a i r e d ,
Also t e s t i n g b l o c k s w i t h large s i n g l e h o l l o w p r e s e n t s
p r o b l e m s . The steel plate used t o d i s t r i b u t e t h e l o a d
o n t h e b locks is p u t o u t o f p l a n e and t h i s i n f l a t e s t h e
91
t h e c r u s h i n g l o a d .
S p e c i f i c a t i o n f o r t h e c h a r a c t e r i s t i c s t r e n g t h of
s a n d c r e t e h o l l o w blocks s h o u l d be based o n s p e c i f y i n g t h e
minimum cross webs and tace s h e l l t h i c k n e s s e s . T h e s e a re
t h e ceometric v a r i a b l e s t h a t g r e a t l y i n f l u e n c e t h e com-
p r e s s i v e s t r e n g t h of h o l l o w b locks n o matter t h e m i x
p r o p o r t i o n .
.. 4.4.2 EFGECTS OF .'\VERAGE SOLAD THICKNESS ON BLOCK S'I'KENGTH
I t h a s b e e n p o i n t e d o u t E " t h a t t h e s o l i d p a r t of
h o l l o w b l o c k i s m o s t significant a n d lt I n f l u e n c e s t h e
s t r e n g t h 05 h o l l o w b l o c k s .
I n t h i s w o r K , e a c n n o l l o w b l o c k t y p e h a v e t h e s a m e
s o l i d bcari-ncj a rea , b u t d i r r e r e n t sum o f t h e l e n g t h s of
t.he c e n t r e - l i n e s of t h e s o l i d p a r t s of t h e b e a r i n g s u r f a c e ,
b e c a u s e of t h e d i f f e r e n c e I n t h e end-web t h i c k n e s s . F o r
a p d r t i c u L < : r hol l o w block t y p e , e .g . j~H12.5-30Hb~, t h e
b e a r i n g a rea is c o n s t a n t . T h e a v e r a g e s o l i d t h i c k n e s s
i n c r e a s e s a s t h e sum o f t h e l e n g t h s of c e n t r e - l i n e s decreases
b e c a u s e of i n c r e a s e In end-web thickness o r a b s e n c e o f
c e n t r e - w e b .
B o t h t h e s t r e n g t h a n d average s o l i d t h i c k n e s s of h o l l o w
b l o c k were e x p r e s s e d a s r a t ios o f t h e c o r r e s p o n d i n g v a l u e s
o f s a n d c r e t e c u b e s p e c i m e n . 'l'he orre relation i s b a s e d o n
h o l l o w b l o c k s w i t n same ena-web t h i c k n e s s . See t a b l e 4.5.0
F i g 4.4. .3 snows c o r r e l a t i o n s b e t w e e n r a t i o o f
s t r e n g t h and r a t i o o t a v e r a g e s o l i d t h i c k n e s s . T h e r e g r e s -
s i o n c u r v e s are e x p o n e n t i a l . T h e c o r r e l a t i o n e q u a t i o n s f o r
t h e d i f f e r e n t g r o u p o f h o l l o w b l o c k s a r c a s f o l l o w s :
F o r 12.3 mm end-web h o l l o w b l o c k s
- 0.3186 e ~ ~ ( 1 . 0 4 4 R t a ) ---- s n (4.4.2.1)
( r = 0.999 s t a n d a r d error = 0.002)
F o r 25 mm end-web b l o c k s
= 0.3172 e x p ( 0 . 9 4 2 Rt,) ---- R s n (4.4.2.2)
(r = 0.382 s t a n d a r d e r r o r = O . U 1 1 )
E'or 3'1.5 rnm end-web b l o c k s
R = 0.2543 e x p ( 1 . & 9 3 R 1 ---- s n t a (4 .4 .2 .3)
(r = 0.992 s t a n d a r d e r r o r = 0 . ~ ~ 9 )
For 50 mm end-web b l o c k s
R s n = U.d4'/2 e x p ( l . 2 5 0 R 1 ----(4.4.2.4) ta
(r = i1.948 s t a n d a r d error 0.021)
f"or 61) mm end-web b l o c k s
R = U.l3b3 exp(2.112 Rta) ---- (4.4.2.5) s n
(r = 0.879 s t a n d a r d error = 0,042)
Where RSn i s t h e r a t i o o f h o l l o w block s t r e n g t h to
c u b e s t r e n g t h and R t a i s the r a t i o of average s o l i d t h i c k n e s s
T a b l e 4.4.2
Block Type
93
Values of R and End-web Thickness
5nd-w b Thickness te (mm)
LE GE NO 0-12.5MM END-WEB BLOCKS a-.-25 . .. . .----
,I 37.5 .
h.-...- 50 .-.-. -.. L C ..
' . - . .-Z-6 - - - F;T- ",.-& 33
3+b -----. -----. 40 28
hATIO OF AYEPAGE SOl.lll TMCKNt S S 1-:1 FIC.;'~+'~ EFFECT OF AVERAGE . SOLO THICKNFSS 01.1 STRENGTH
o f c u b e .
The f i v e d i f f e r e n t end-web hollow b l o c k s s t u d i e d ,
showed a h i g h d e g r e e o f c o r r e l a t i o n between the r a t i o o f
s t r e n g t h a n d t h e r a t i o o f a v e r a g e s o l i d t h i c k n e s s .
Eze-Uzomaka (27) h a v e shown t h a t the e x p o n e n t i a l c o r r e l a -
t i o n b e t w e e n r a t i o o f s t r e n g t h a n a r a t i o of averaqe
s o l i d t h i c k n e s s t o be of t h e form:
(r' = u.Y'/ s t a n a a r d error 0.05)
w h e r e R i s t h e r a t i o o t s t r e n g t h i n r e l a t i o n to s g
g e o m e t r y e f f e c t ,?nd H i s t h e r a t i o of t h i c k n e s s . t
T h i s i s i n a g r e e m e n t w i t h e q u a t i o n 4.4.2-4 w h i c h
d e s c r i b e s t h e e x p o n e n t i a l r e l n t l o n s h i p b e t w e e n r a t i o
o f s t r e n g t h and r a t i o of average s o l i d t h i c k n e s s for
50 mm end-web h o l . 1 0 ~ blocks. The d i s c r e p a n c y i n the
v a l u e o f c o n s t a n t s may be d u e t o the d i f t e r e n c e i n
s t r e n g t h and a v e r a g e solid t h i c k n e s s to which t h e two
e q u a t i o n s were expressed. Eze-Uzomaka ' 2 7 ) e x p r e s s e d
b o t h thc s t r e n g t h ana average s o l i d t h i c k n e s s o f a h o l l o w
block t y$e a s r < l t l o s of the c o r r e s p o n d i n g values f o r one
o r t h e ~ ~ o c k ty7cs. I n t h i s study, b o t h the s t r e n g t h
and avc!r~lc_le so l i d . t h i c k n e s s of h o l l o w block were
e x p r e s s e d a s r a t i o s of t h e c o r r e s p o n d i n g v a l u e s of
s a n d c r e t e c u b e s p e c i m e n .
We t h e n , c o n c l u d e t h a t t h e t h i c k n e s s of t h e
s o l i d p a r t s o f a h o l l o w b l o c k a f f e c t s t h e s t r e n g t h
o f b l o c k s , t h e s t r e n g t h i n c r e a s e s e x p o n e n t i a l l y w i t h
i n c r e a s e i n t h e ave r age s o l i d t h i c k n e s s of b l o c k s .
4.5 EFFECT OF
29 N e v i l l e o b s e r v e d
( s o l i d v o l u m e ) l eads t o
HOLLOW VOLUME
t h a t g r e a t e r v o l u m e of s p e c i m e n
a more u n i f o r m stress d i - s t r i b u -
t i o n a n d t h e r e f o r e a lesser likelihood of p r e m a t u r e
: f a i l u r e . T h e i n t r o d u c t i o n of c a v i t y i n a s p e c i m e n
r e d u c e s t h e a v a i l a b l e s o l i d v o l u m e fo r u n i t o r m stress
d i s t r i b u t i o n w h i c h may lead to p r e m a t u r e f a i l u r e . I t
i s a l s o ~ e a s o n a b l e t o a s s u m e t h a t t h e l a r g e r v o l u m e of
s a n d c r e t e s u b j e c t e d to stress, t h e m o r e l i k e l y i t i s t o
c o n t a i n e l e m e n t o f a g i v e n e x t r e m e ( l o w ) s t r e n g t h w h i c h
is a r e s u l t of d i f f e r e n t i a l c u r i n g ra tes of t h e v a r i o u s
s izes o f s p e c i m e n s , a n d d i f f e r e n c e i n t h e q u a l i t y of t h e
mater ia l as-cast i n t o d i f f e r e n t s i z e o f m o u l d s (workman-
s h i p ) .
H o l l o w b l o c k i s c o m p o s e d o f webs a n d face s h e l l s
w h i c h h a v e d i f f e r e n t d i m e n s i o n s . A s t h e h o l l o w v o l u m e
i n c r e a s e s , t h e s e webs a n d face s h e l l s d e c r e a s e a c c o r d i n g l y .
T h e m e a s u r e d s t r e n g t h of h o l l o w b l o c k s decreases a s t h e
t h i c k n e s s o f t h e a g g r e g a t i n g h o l l o w block g e o m e t r y de-
crease i.c. i n c r e a s e i n v o l u m e of h o l l o w r e d u c e s t h e
s t r e n y t h o f b l o c k .
I n t h c r e m a l n i n y p j r t oi t h l s s e c t l o n , we s h a l l
p r e s e n t the r e s u l t o f regression a n a l y s l s b e t w e e n t h e
compressive s t r e n g t h a n d t h e h o l l o w v o l u m e ( V ) t o s o l i d 0
v o l u m e ( V s ) r a t i o ( V o / V s ) for the d i t f e r e n t s t r e n g t h
C o m p u t a t i o n s a s shown i n table 4.5.0. Fig. 4.3.u snows
t h e g e o m e t r i c r e g r e s s i o n C u r v e s b e t w e e n s t r e n g t h a n d
h o l l o w v o l u m e to so l i d v o l u m e r a t i o ( V / V s ) t o r t h e s i d e 0
s u r f a c e g r o s s area s t r e n g t h a n d t h e as-cast s u r f a c e n e t
a rea s t r e n g t h . T h e y a r e d e s c r i b e d b y t h e r o l l o w i n y
c o r r e l a t i o n p o w e r e q u a t i o n s :
o r 1 2 . s , mrn end-web b l o c k s
Z ( r =- ~ ~ ~ 9 9 6 s t a n d a r d error = O . U l ' / N / m m )
L ( r = 0.963'/ s t a n d a r d error = 0.Z41Njmm )
For 2 3 rnm end-web b l o c k s
2 ( r = U . Y ~ U s t a n d a r d error 0.108N/mm
L ( r = U . Y I ~ s t a n d a r d error = 0.36'1 N/mm
F o r 3'1.3 rnm end-web b l o c k s
Z ( r ' 0.990 s t a n d a r d error = 0.097N/mm )
L ( r = 0.9'95 s t a n d a r d error = 0 . 1 0 0 N / m m )
Block Type
FIG/*,5.0 EFFECT OF V O L W E ON COMPRESSIVE SfRENGTH . -.
F o r 5 0 mrn end-web b l o c k s
2 ( r = 0.946 s t a n d a r d error = 0.149~/mrn
2 ( r = 0.993 s t a n d a r d error = 0 . 0 8 3 N / m m )
F o r bO mm end-web b l o c k s
2 ( r = U.Y'/Y s t a n a a r d c r r o r = U.124N/mm )
2' ( r = 0.941 s t a n d a r d error = 01317N/mm
F i g 4.5.1 shows t h e best g e o m e t r i c c u r v e t h r o u g h a l l
t h e d a t a , f o r t h e d i f f e r e n t s t r e n g t h c o m p u t a t i o n s a n d are
g i v e n by t h e f o l l o w i n g g e o m e t r i c e q u a t i o n s :
2 ( r = 0.809 s t a n d a r d e r r o r = 0.293N/mm )
f = 1 . ~ 9 ~ ( V / v s ) -0.061 ---- xg 0
( 4 . 5 . 1 2 )
2 ( r = 0 , 8 6 1 s t a n d a r d error = 0.345N/mm )
T h c s t r e n g t h was f o u n d t o be i n v e r s e l y p r o p o r t i o n a l
to t h e hol lov: volume. I t a l s o showed a h i g h l y s i g n i f i c a n t
c o r r e l a t i o n Ccefr lc l e n t , when s e p a r a t e g e o m e t r i c c u r v e s are
d r a w n t h r o u g h t h e i n d i v i d u a l sets.
F o r t h e a s - c a s t s u r f a c e n e t a r e a s t r e n g t h , t h e
l o r r e l a t i o n c o e f f i c i e n t r anges f rom u. r4sb-0 .9996, and t h e
A i5OMM " .. w
b W M .. 1.
\\ *, o125MM END-WEB BLOCKS STRENGTH "9
925MM 'A
C .. \ 437-5hlM - .. \ VSOMM - a . 0
\ t 6 0 M M .. w w ,# '. t '1
-.4 -_ 8
B -_ 3 - - -.- 0 b - --- 1
-- -
0$----7b- --'
RATIO OF VOLU fF f U / V ~ l ' / o .----3P
FIG 4.5.1 EFFECT OF VOLUME ON COMPRESSIVE STRENGTH
2 s t a n d a r d error v a r l r s f r o m U . ~ l ' / ~ / m m ~ - " . 1 4 9 ~ / m r n . W h i l e
t h e b e s t g e o i n e t r i c c u r v e t h r o u g h a l l t h e d a t a h a s a
c o r r e l a t i o n c o e f f i c i e n t of 0.809 a n d s t a n d a r d error o f
2 0.293N/mm .
F o r t h e side s u r f a c e g r o s s a rea s t r e n g t h , t h e
c o r r e l a t i o n cceff i c i . e n t r a n q e s f rom 0.9lb8-O.!J92 a n d t h e
T h e bes t g e o m e t r i c c u r v e t h r o u g h all the d a t a h a s a
c o r r e l a t i o n c o e f f i c i e n t of U.8bl and .standard error o f
2 0,345N/mm .
T h e by-st g e o m e t r i c c u r v e t h r o u g h a l l t h e d a t a snowed
s i g n i . f l c a n t : c o r r e l c i t l o n c o e f f i c i e n t i n b o t h cases. B u t t n e
i n v e r s e p r o p o r t i o n between strength a n d h o l l o w v o l u m e is
bett-er d e s c r i D e d b y gcome t r i c curve t h r o u g h i n d i v i d u a l
sets. Ne, t h e n c o n c l u d e t h a t hollow v o l u m e a f f e c t s t h e
s t r e n q t h , t h e s t r e n g t h i s i n v e r s e l y p r o p o r t i o n a l t o t n e
h o l l o w v o l u m e .
F i g 4.5 . L s h o w s t h e p a r a u o l i c r e g r e s s i o n c u r v e s
b e t w e e n t h? s l u e s u r r d c e n e t area s t r e n g t h and t he h o l l o w
v o l u m e . T h e y sre d e s c r i b e d b y t h e follawlng r e g r e s s i o n
e q u a t i o n s :
t ' o r 1 2 . 5 rnm end-web b l o c k s
( r = O.YU69 s t a n d a r d error = ~ . 2 1 0 4 ~ / r n m ~ )
b'or 2 3 mm end-web blocks
2 ( r = u . ~ ' / 8 1 s tandard e r r o r = 0.3645N/mm )
For 37.5 mm end-web b locks
2 txn = 9.0739-7-7484 (Vo /Vs ) + 2.9734(Vo/Vs) ---(4.5.15)
2 ( r = 0.9511 s t anda rd e r r o r = 0.558N/mm 9 -
For 50 mm end-web b locks
(r = 1,000 s t anda rd e r r o r = 0.00)
For 60 mm end-web b locks
2 f = 12.7401-23.4504(Vo/Vs + 14.9394(Vo/VS) ---(0.5.17)
xn 2
( r = 0.09981 s t anda rd e r r o r = 0.0794N/mm
t h a t d e s c r i b e t h e c o r r e l a t i o n between s i d e . s u r f a c e n e t a r e a
s t r e n g t h and the hollow volume t o solid volume r a t i o ( V o / V s )
a r e h igh ly s i g n i f i c a n t . I t ranges from 0.9511-1.00 and has 2
s t anda rd e r r o r range of 0.00-0.558N/mm . This shows t h a t f o r b locks of d i f f e r e n t end-web thick-
ness, t h e r e i s a minimum s t r e n g t h and a corresponding hollow
volume t o s o l i d volume r a t i o ( V o / V S ) . Th is is shown i n
t a b l e 4.5.1.
LEGFPQ o12.5MM END-WE9 BLOCKS a25hlh!
0 A 375t.lb1
, . I /
/ I /;/ / !
,, / ' ,' 7' '. i -. . -- - -4 -----...---'-A
L-r-- - - +
FG4.5-2 EFFECT
T a b l e 4.5.1 Minimum Side S u r f a c e Net Area S t r e n g t h a n d T h e C o r r e s p o n d i n g H o l l o w Volume t o S o l i d Volume Ratio (Vo/VS).
Minimum S t r e n g t h I H o l l o w to Sol i d ( ~ / m m ~ ) T h i c k n e s s Volume Ratio.
i
5.0 CONCLUSIONS AND RECOMMENDATIONS
5 . 1 CONCLUSIONS
S t a t i s t i c a l v a r i a t i o n i n c o m p r e s s i v e s t r e n g t h o f
h o l l o w s a n d c r e t e b l o c k s c o n f i r m s t h e o b s e r v a t i o n t h a t t h e
s t a n d a r d d e v i a t i o n a n d c o e f f i c i e n t of v a r i a t i o n is n o t
c o n s t a n t f o r d i f f e r e n t s t r e n g t h l e v e l s ; a n d t h e d i f f e r e n c e
i n t h e d i r e c t i o n o f l o a d i n g o f t h e h o l l o w b l o c k i n f l u e n c e s
t h e d i f f e r e n c e i n s t a n d a r d d e v i a t i o n a n d c o e f f i c i e n t o f
v a r i a t i o n i n as-cast t e s t e d h o l l o w b l o c k s a n d s ide way
t e s t e d h o l l o w b l o c k s .
T h e n e t area s t r e n g t h s h o w e d lower coeff ic fent of
v a r i a t i o n t h a n g r o s s a r e a s t r e n g t h . T h i s means tha t
s t r e n q t h a a l c u l a t e d o n t h e b a s i s of n e t area shows u n i f o r -
m i t y a n d b e t t e r q u a l i t y i n p r o d u c t i o n .
V a r i o u s c o m p r e s s i v e s t r e n g t h when compared w i t h
c y l i n d e r s t r e n g t h s h o w e d t h a t t h e n e t area s t r e n g t h c a l c u l a -
t i o n i s better t h a n t h e g r o s s area s t r e n g t h c a l c u l a t i o n .
F o r 30H12.5-30H60 h o l l o w b l o c k s t e s t e d as-cast, n e t area
s t r e n g t h g i v e s better s t r e n g t h c a l c u l a t i o n a t 0 .02 s i g n i f i -
c a n c e l e v e l . F o r 40.7H12.5-40.7H60, 50H12.5-50H60 a n d
60H12.5-60H45 h o l l o w b l o c k s tested side w a y s , n e t a r e a g i v e s
better s t r e n g t h c a l c u l a t i o n a t 0 .02 s i g n i f i c a n c e l e v e l .
C o r r e l a t i o n b e t w e e n s t r e n g t h o b t a i n e d by l o a d i n g o n
t h e two p e r p e n d i c u l a r s u r f a c e s o f h o l l o w b l o c k s , showed
a l i n e a r c o r r e l a t i o n . T h i s l i n e a r c o r r e l a t i o n is b e t t e r
d e s c r i b e d b y best s t r a i g h t l i n e t h r o u g h t h e i n d i v i d u a l
sets of h o l l o w b l o c k s e a c h w i t h i t s own s l o p e .
T h e i n c l u s i o n o f t h e c e n t r e - w e b to end-web r a t i o ( u )
i n t h e C o r r e l a t i o n b e t w e e n s t r e n g t h s o n t h e t w o p e r p e n d i c u l a r
s u r f a c e s b y mu1 t i p l e r e g r e s s i o n a n a l y s i s is h i g h l y s i g n i f i-
c a n t t h a n l i n e a r c o r r e l a t i o n ,
T h e r e is no u n i v e r s a l constant rat io and d i f f e r e n c e
b e t w e e n t h e c r u s h i n g l o a d s obtained by l oad ing o n t h e two
p e r p e n d i c u l a r s u r f a c e of hollow Blocks. They are c o n s t a n t
f o r e a c h h o l l o w b l o c k .
T h e e f f e c t o f centre-web to end-web r a t i o o n t h e
c o m p r e s s i v e s t r e n g t h i n d i c a t e s a p a r a b o l i c r e l a t i o n s h i p
w i t h maximum s t r e n g t h a n d t h e corresponding c e n t r e - w e b
t o end-web ra t io .
T h i s s t u d y c o n f i r rns ~ z e - ~ z o m a k a ' s * ~ o b s e r v a t i o n t h a t
t h e t h i c k n e s s of t h e s o l i d p a r t o f a h o l l o w b l o c k a f f e c t s
t h e s t r e n g t h of b l o c k s , t h e s t r e n g t h i n c r e a s e s e x p o n e n t i a l l y
w i t h i r l c r e a s e i n t h e a v e r a g e s o l i d t h i c k n e s s o f b l o c k s ,
A l s o , c o r r e l a t i o n b e t w e e n s t r e n g t h a n d a v e r a g e s o l i d t h i c k n e s s
i s b e t t e r d e s c r i b e d by best e x p o n e n t i a l c u r v e t h r o u g h
i n d i v i d u a l sets o f h o l l o w b l o c k s w i t h t h e same end-web
t h i c k n e s s .
The h o l l o w vo lume affects t h e s t r e n g t h , t h e s t r e n g t h
i s i n v e r s e l y p r o p o r t i o n a l t o t h e h o l l o w volume. T h e
s t r e n g t h d e c r e a s e s a s h o l l o w v o l u m e increases. The i n v e r s e
p r o p o r t i o n b e t w e e n s t r e n g t h a n d h o l l o w volume is o n l y
d e p i c t e d b y as-cast s u r f a c e n e t area s trength , g r o s s area
s t r e n g t h a n d t h e g r o s s area s t r e n g t h of h o l l o w b l o c k s
t e s t e d s i d e ways. T h i s i n v e r s e proportion is b e t t e r
d e s c r i b e d b y g e o m e t r i c c u r v e t h r o u g h i n d i v i d u a l sets w i t h
t h e same end-web t h i c k n e s s .
T h e e f f e c t o f h o l l o w v o l u m e o n t h e n e t area s t r e n g t h
o f h o l l o w b l o c k s t e s t e d s i d e ways i n d i c a t e s a p a r a b o l i c
r e l a t i o n s h i p w i t h minimum s t r e n g t h a n d the c ~ r r e s p o n d i n g
- , h o l l o w Golume for holl:,w b l o c k s w i t h t h e same end-web
th icknc-sr;.
S i n c e , n e t a r e a s kreng t h s showed lower coaff ic=it?nt
o f v a r i a t i o n t h a n g r o s s area s t r e n g t h s , i t is better to
c a l c u l a t e t h e c o m p r e s s i v e s t r e n g t h o f h o l l o w s a n d c r e t e
block o n t h e basis o f n e t area.
I t i s a d v i s a b l e , to d e f i n e the c h a r a c t e r i s t i c s t r e n g t h
o f h o l l o w s a n d c r e t e b l o c k s base o n t h e m u l t i p l e c o r r e l a t i o n
b e t w e e n t h e n e t arcd s t r e n g t h sf h o l l o w blocks t c s t c d
a s - c a s t , Chc n e t a r e a s t r e n g t h o f h o l l o w b l o c k s t e s t e d
s i d e ways a n d t h e c e n t r e - w e b t o end-web r a t i o o f h o l l o w
b l o c k s . T h i s w i l l e l i m i n a t e c a p p i n g , g r i n d i n g o r p a c k i n g
w i t h b e d d i n g m a t e r i a l r e q u i r e d f o r c o m p r e s s i o n tests o n
as-cast s u r f a c e s .
T h e r e i s need t o m a n u f a c t u r e h o l l o w b l o c k s w i t h t h e
c e n t r e - w e b b e i n g g r e a t e r t h a n t h e end-web i n o r d e r to
.. e n s u r e h i g h e r s t r e n g t h .
Minimum s t r e n g t h c a n be s p e c i f i e d fo r h o l l o w s a n d c r e t e
b l o c k s a c c o r d i n s t o t h e end-web t h i c k n e s s as shown b y t h e
h o l l o w vo lume e f f e c t s o n n e t a r e a s t r e n g t h of h o l l o w b l o c k s
t e s t e d s i d e ways. The e q u i v a l e n t as-cast net area s t r e n g t h
is o b t a i n e d b y u s i n g n e c e s s a r y r e l a t i o n s h i p b e t w e e n s t r e n g t h s
. o n t h e fwo p e r p e n d i c u l a r s u r f a c e s .
A l t h o u g h , 60H12-60H45 h o l l o w b l o c k s showed h i g h
C.ornpressive s t r e n g t h v a l u e s , t h e i r b e h a v i o u r a n d f a i l u r e
p a t t e r n when u n d e r c o m p r e s s i o n make them u n s t a b l e f o r a n y
l o a d - b e a r i n g wall c o n s t r u c t i o n . They are good o n l y f o r
t h e non- l o a d - b e a r i n g w a l l s .
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14 . EZE-UZOMAKA, O.J. "An A p p r a i s a l of Method of T e s t i n g Some P h y s i c a l P r o p e r t i e s of Sand- c re te B l o c k s l l , Proceedings, I n s t i t u t i o n o f Civil E n g i n e e r s , P a r t 2 , ( G O ) , vol. 63, S e p t , 1 9 7 7 , p p 625 - 639.
15. O S I L I , I , " S a n d c r e t e ( U n p u b l i s h e d R e p o r t ) , M i n i s t r y o f Works a n d Housing, L a g o s , '1962.
3.6. SF'EDEUE, A.E. " R o l e o f Government Agencies i n P r o t e c t i n g t h e Public Against S u b s t a n d a r d P r o t e c t s l f , P r o c e e d i n g o f Symposium o n S a n d c r e t e Block a n d t h e C o n s t r u c t i o n I n d u s t r y , D e p a r t m e n t of C i v i l E n a i n p p r i n a , U n i v e r s i t y of N i g e r i a , Nsukka, A u g u s t , 1 9 7 5 , pp 1 0 5 - 111.
KOPYCINSK, U. a n d e t a1 " O r d i n a r y C o n c r e t e 1 ' , Arkady , 19'78.
RECOMMENDATION O F COMMITTEE ON REVIEW OF DECISION. P r o c e e d i n g o f t h e C o n f e r e n c e o n M a t e r i a l T e s t i n g , C o n t r o l and R e s e a r c h ; F e d e r a l M i n i s t r y o f Works a n d H o u s i n g , L a g o s , Feb, 1 9 7 9 , pp 102 .
ONYEMELUKNE, 3 -0. t T o n s t r u c t i o n E x p e r i e n c e w i t h S a n d c r e t e B l o c k s l l , P r o c e e d i n g o f Symposium o n S a n d c r e t e Block a n d t h e C o n s t r u c t i o n I n d u s t r y , D e p a r t m e n t o f C i v i l E n g i n e e r i n g , U n i v e r s i t y o f N i g e r i a , Nsukka, A u g u s t 1375.
EZE-UZOMAKA, O . J . "The C r u s h i n g Strength of S a n d c r e t e B l o c k s I n R e l a t i o n to t h e i r P r o d u c t i o n a n d Q u a l i t y C o n t r o l " , op. c i t .
EZE-uZOMAKA, O . J . ' ' D i s c u s s i o n o f R e f e r e n c e 14", P r o c e e d i n g s , I n s t i t u t i o n of C i v i l Enqinemrg Pact 2 [GB) , vol. 65, June 1478 pp 441-495.
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EZE-UZOMAKA, 0. J . l1Non-des t ruc t ive Assessment of t h e Structura l Suitability o f h a d - Bearing Blocks8 ' , C o n s t r u c t i o n Research I n t e r n a t i o n a l , Proceedings of t h e S e v e n t h CIB T r i e n n i a l Congress E d i n b u r t h , vol . 1, S e p t . 1977, pp 183 - 190; 420 - 424.
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25. HUGHES, B, P , a n d BRHRAMIAN, B, llSame F a c t o r s A f f e c t i n g t h e C o m p r e s s i v e S t r e n g t h o f C o n c r e t e " . Maqazine o f C o n c r e t e R e s e a r c h , V o l 1 9 , No. 6 0 S e p t . 1967.
26. GLUCKLISH, J. " F r a c t u r e o f P l a i n C o n c r e t e w , J o u r n a l o f E n g i n e e r i n g M e c h a n i c s D i v i s i o n , ASCE, V o l , 89, 1 9 6 3 , pp 1 3 3 ,
27 , EZE-UZOMAKA, O.J. I1Some F a c t o r s which A f f e c t t h e C r u s h i n g S t r e n g t h o f S a n d c r e t e B l o c k s n , M a t e r i a u x e t C o n s t r u c t i o n s , v o l . 1 0 No, 55 , 1 9 7 7 , pp 45 - 48.
28. VILLA, I. S . "The E f f e c t o f Mix P r o p o r t i o n and C u r i n g C o n d i t i o n o n S h r i n k a g e o f
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p p 8 7 - 90.
29, NEVILLE, A. M. l tA G e n e r a l R e l a t i o n for S t r e n g t h s o f C o n c r e t e S p e c i m e n s of Different S h a p e s a n d Sizesw, A C I J o u r n a l , ? r o c e e d i . n g s , vol . 63 N o . 10 O c t o b e r 1?66, p p 1 0 9 5 - 1110.
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33 . MURDOCK, L. J. "The C o n t r o l of C o n c r e t e Q u a l i t y " , P r o c e e d i n g s , I n s t i t u t i o n o f C i v i l E n g i n e e r s , L o n d o n , E n g l a n d , P a r t 1 v o l . 2, No. 4 , J u l y 1953.
ACI COr4MITTEE 2 1 4 flRecommended P r a c t i c e f o r E v a l u a t i o n o f C o m p r e s s i o n T e s t R e s u l t n o f C o n c r e t e " , A m e r i c a n C o n c r e t e I n s t i t u t e , Det roi t , M i c h , 1965.
35. WILLIAPI, V. " A p p l i e d S t a t i s t ics f o r E n g i n e e r s f 1 McGraw-Hi l l , New Y o r k , 2nd E d i t i o n , 1'363.
36. OL,%,JURE, A . A . f l , s t a t i S t . i c z l A n a . l y s i s o f C o n c r e t e C u b e S t r e n g t h f ' , F e d e r a l M i n i s t r y of Works a n d H o u s i n g 1 7 t h A n n u a l C o n f e r e n c e o n Mater ia l T e s t i n g , C o n L r o l a n d H e s e a r c h , L a g o s , 3.985, pp 68 - 74.
FIG. 3
D.F.
Probability d a larger value of r
t Abridged horn TYMC VI OI Statistical Tnblen for IIiokgiii(ld, Agricultural and /
Mrdicsl 1tcwatc:h by R. A. F i h ~ m d Frnnk Ytrlcn, Oliver & Boyd, Ltd., IpUjn- J
burgh rn~d London, 1953, reprinted with penillssion of puldiulicrs.
0.01 prob~tbility of a lrtrger vahc of F urn - degrees or lrcedorn lor lillrncralor
*I - dryrcca uf Irt.nlum fur dcaonsi~~utor
- 3
-.,
.4ID 1). 17
d. 113 2.06
I). 7s 11.45 7.5'J 0. U'J
6.53
:. T! 3.193 6.74 5.56 5.42
5.21 b , t t &.0! 5.01 4.U.
4.X' 1.1: 4.71 4,7' 4, 11,
- 4 - 5,625 !Kl. ?S 28. 7I 15.UU 11.3U
u. IS 7.115 7.01 ti. 42 L.UM
5. d? S.Ik 5.20 s.m:I 4 . w
4.77 4.07 4 . M 4.51 4.43
4.3; 4.31 4 . 3 4.2: 4.11
8 9 -- 5.081 6.022 B0.M 911.38 27.49 27.34 14.80 14.80 10.27 LO. 16
8. LO 7.08 0.84 0.71 O.&? 5.01 5.47 5.45 5.06 4.U5
4.74 4.63 4 . M 4.30 1.30 4.19 4.14 LO'J 4 . w S.RU
a.80 5.78 3.79 3.08 3.71 3.80 3.83 3.52 3.56 3.45
3.51 3.40 3.45 3.35 3.41 3.30 3.30 3.25 3.32 3.21
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I
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10
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PI dearw or freedom lor denon~inawr
I I
.-
?43 9.4U 8.76 5.03 4, ill
4.03 3.60 3.31 :I. 10 2. U-l
I. R.' t. 72 2.61 2.58 2 .51
2.15 2.41 2.97 2.31 2.31
2.28 2.28 9.24 2.?P 2.20
1
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l.8G I.X'2 1.76 1.74 1.6'3 1.07 1.04 1.61 1.114 1.80 8-74 1.71 1.87 1.111 1.l11 1.6U 1.82 1.711 1 . n 1.m 1.u 1.a 1 . m r . s i 1.80 1.10 I , ?& k.U1 1.0:i 1.110 1.57 1.51 1.70 1.51 I.l@ I.06 1.81 I.bU 1.10 1 . U
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1.f2 1.87 L B I 1.68 1.52 -1.h 1.48 I,+:! 1,741 1.86 l.b* 1.60 I.bU I.4X 1 . 4 1.41 1 ,M 1-03 1.57 I S M 1.4!l t .4& 1-42 1.39 1.67 1.8.2 1.54 1.53 1.47 1.45 1.10 1.37 .I.U 1.40 1.84 1.51 1.45 1.42 1.36 1.35 1.63 I d 7 1-51 1.48 1.42 1.90 1.3.1 1.90
1.80 1.58 1.49 1,15,1.30 1.36 1.31, 1.27 I.S9 1.54 1.41 1.44 1,37 t.34 1.20,l.:: 1.5; 1.52 1 3 5 1.12 1.35 1.20 1,:" 1.54 ,I.40 1.42 1.3% l..X 1 . 3 1.?2 1.16 I .X l 1.47 1.41 1.311 1.30 l . ? D 1.1!1 1.1:1 I +I I 46: I A n 9 !I5 I . 3 I ?A 1 B 17 I I I